Analysis of PDEs
New submissions
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New submissions for Wed, 8 May 24
- [1] arXiv:2405.03791 [pdf, ps, other]
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Title: Regularity for Fully Nonlinear Elliptic Equations with Natural Growth in Gradient and Singular NonlinearitySubjects: Analysis of PDEs (math.AP)
In this article we consider the following boundary value problem
\begin{equation*}\label{abs} \left\{ \begin{aligned} F(x,u,Du,D^{2}u)+c(x)u+ p(x)u^{-\alpha}&=0~\text{in}~\Omega\\ u&=0~~\text{on}~~\partial\Omega, \end{aligned} \right. \end{equation*} where $\Omega$ is a bounded and $C^{2}$ smooth domain in $\mathbb{R}^N$ and $F$ has superlinear growth in gradient and $c(c)<-c_{0}$ for some positive constant $c_{0}.$ Here, we studies the boundary behaviour of the solutions to above equation and establishes the global regularity result similar to one established in [12,16] with linear growth in gradient. - [2] arXiv:2405.03802 [pdf, ps, other]
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Title: A note on Hölder regularity of weak solutions to linear elliptic equationsAuthors: Karthik AdimurthiSubjects: Analysis of PDEs (math.AP)
In this paper, we show that weak solutions of $$-\text{div} \mathbb{A}(x)\nabla u = 0 \qquad \text{where}\quad \mathbb{A}(x)= \mathbb{A}(x)^T \,\, \text{and} \,\, \lambda |\zeta|^2 \leq \langle \mathbb{A}(x)\zeta,\zeta\rangle \leq \Lambda |\zeta|^2,$$
and $\mathbb{A}(x) \equiv \mathbb{A}$ is a constant matrix are H\"older continuous $u \in C^{\alpha}_{\text{loc}}$ with $\alpha \geq \frac12 \left(-(n-2) + \sqrt{(n-2)^2 + \frac{4(n-1)\lambda}{\Lambda}} \right)$. This implies that the example constructed by Piccinini - Spagnolo is sharp in the class of constant matrices $\mathbb{A}(x) \equiv \mathbb{A}$. The proof of H\"older regularity does not go through a reduction of oscillation type argument and instead is achieved through a monotonicity formula.
In the case of general matrices $\mathbb{A}(x)$, we obtain the same regularity under some additional hypothesis. - [3] arXiv:2405.03871 [pdf, ps, other]
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Title: Nonlinear Schrödinger-Poisson systems in dimension two: the zero mass caseSubjects: Analysis of PDEs (math.AP)
We provide an existence result for a Schr\"odinger-Poisson system in gradient form, set in the whole plane, in the case of zero mass. Since the setting is limiting for the Sobolev embedding, we admit nonlinearities with subcritical or critical growth in the sense of Trudinger-Moser. In particular, the absence of the mass term requires a nonstandard functional framework, based on homogeneous Sobolev spaces. These features, combined with the logarithmic behaviour of the kernel of the Poisson equation, make the analysis delicate, since standard variational tools cannot be applied. The system is solved by considering the corresponding logarithmic Choquard equation. We prove the existence of a mountain pass-type solution via a careful analysis on specific Cerami sequences, whose boundedness is achieved by exploiting an appropriate functional, obtained by evaluating the energy functional on particular paths.
- [4] arXiv:2405.03909 [pdf, ps, other]
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Title: Stability of traveling waves in non-cooperative systems with nonlocal dispersal of equal diffusivitiesSubjects: Analysis of PDEs (math.AP)
In this work, we first prove a stability theorem for traveling waves in a class of non-cooperative reaction-diffusion systems with nonlocal dispersal of equal diffusivities. Our stability criterion is in the sense that the initial perturbation is such that a suitable weighted relative entropy function is bounded and integrable. Then we apply our main theorem to derive the stability of traveling waves for some specific examples of non-cooperative systems arising in ecology and epidemiology.
- [5] arXiv:2405.03982 [pdf, ps, other]
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Title: Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifoldsComments: 18 pages. Comments welcome!Subjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywhere on the domain.
- [6] arXiv:2405.03984 [pdf, ps, other]
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Title: Inhomogeneous wave kinetic equation and its hierarchy in polynomially weighted $L^\infty$ spacesComments: 40 pagesSubjects: Analysis of PDEs (math.AP)
Inspired by ideas stemming from the analysis of the Boltzmann equation, in this paper we expand well-posedness theory of the spatially inhomogeneous 4-wave kinetic equation, and also analyze an infinite hierarchy of PDE associated with this nonlinear equation. More precisely, we show global in time well-posedness of the spatially inhomogeneous 4-wave kinetic equation for polynomially decaying initial data. For the associated infinite hierarchy, we construct global in time solutions using the solutions of the wave kinetic equation and the Hewitt-Savage theorem. Uniqueness of these solutions is proved by using a combinatorial board game argument tailored to this context, which allows us to control the factorial growth of the Dyson series.
- [7] arXiv:2405.04014 [pdf, ps, other]
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Title: On the uniqueness of the mild solution of the critical quasi-geostrophic equationComments: 13 pagesSubjects: Analysis of PDEs (math.AP)
We demonstrate that the uniqueness of the mild solution of the two-dimensional quasi-geostrophic equation with the critical dissipation holds in the scaling critical homogeneous Besov space $\dot{B}^0_{\infty,1}$. We consider a solustion of integral equation, and our result does not need regularity assumption.
- [8] arXiv:2405.04070 [pdf, other]
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Title: Weak and Perron's Solutions to Linear Kinetic Fokker-Planck Equations of Divergence Form in Bounded DomainsComments: 39 pagesSubjects: Analysis of PDEs (math.AP)
In this paper, we investigate weak solutions and Perron-Wiener-Brelot solutions to the linear kinetic Fokker-Planck equation in bounded domains. We establish the existence of weak solutions by applying the Lions-Lax-Milgram theorem and the vanishing viscosity method in product domains. Additionally, we demonstrate the regularity of weak solutions and establish a strong maximum principle. Furthermore, we construct a Perron solution and provide examples of barriers in arbitrary bounded domains. Our findings are based on recent advancements in the theory of kinetic Fokker-Planck equations with rough coefficients, particularly focusing on the characterization of a weaker notion of trace defined through convolution-translation.
- [9] arXiv:2405.04084 [pdf, ps, other]
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Title: Existence and dynamical behaviour of vectorial standing waves with prescribed mass for Hartree-Fock type systemsSubjects: Analysis of PDEs (math.AP)
In this paper, we investigate vectorial standing waves with prescribed mass for the Hartree-Fock type system (HF system) with the double coupled feature. Such system is viewed as an approximation of the Coulomb system with two particles appeared in quantum mechanics. By exploring the interaction of the double coupled terms, we prove the exis?tence/nonexistence and symmetry of vectorial energy ground states for the corresponding stationary problem. Furthermore, we obtain the relation between vectorial energy ground states and vectorial action ground states in some cases. Finally, we establish conditions for global well-posedness and finite time blow-up to HF system with the initial data, and prove orbital stability/strong instability of standing waves.
- [10] arXiv:2405.04123 [pdf, ps, other]
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Title: Two uniqueness results in the inverse boundary value problem for the weighted p-Laplace equationSubjects: Analysis of PDEs (math.AP)
In this paper we prove a general uniqueness result in the inverse boundary value problem for the weighted p-Laplace equation in the plane, with smooth weights. We also prove a uniqueness result in dimension 3 and higher, for real analytic weights that are subject to a smallness condition on one of their directional derivatives. Both results are obtained by linearizing the equation at a solution without critical points. This unknown solution is then recovered, together with the unknown weight.
- [11] arXiv:2405.04268 [pdf, ps, other]
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Title: Dynamics of an epidemic model with nonlocal di?usion and a free boundarySubjects: Analysis of PDEs (math.AP)
An epidemic model, where the dispersal is approximated by nonlocal diffusion operator and spatial domain has one ?xed boundary and one free boundary, is considered in this paper. Firstly, using some elementary analysis instead of variational characterization, we show the existence and asymptotic behaviors of the principal eigenvalue of a cooperative system which can be used to characterize more epidemic models, not just ours. Then we study the existence, uniqueness and stability of a related steady state problem. Finally, we obtain a rather complete understanding for long time behaviors, spreading-vanishing dichotomy, criteria for spreading and vanishing, and spreading speed. Particularly, we prove that the asymptotic spreading speed of solution component (u; v) is equal to the spreading speed of free boundary which is ?nite if and only if a threshold condition holds for kernel functions.
- [12] arXiv:2405.04298 [pdf, ps, other]
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Title: Multiplicity results for critical fractional Ambrosetti-Prodi type system with nonlinearities interacting with the spectrumAuthors: Eduardo. H. Caqui (1), Sandra M. de S. Lima (2), Fábio R. Pereira (3) ((1) Departamento de Ciencias Sede Brena, Universidad Privada del Norte, Cercado de Lima, Lima, Peru (2) Departamento de Ciências Exatas, Biológicas e da Terra, INFES-UFF, Santo Antônio de Pádua - RJ, Brazil (3) Departamento de Matemática, Instituto de Ciências Exatas, Universidade Federal de Juiz de Fora, Juiz de Fora - MG, Brazil)Comments: 33 pages. F. R. Pereira was supported partially by FAPEMIG/Brazil (RED-00133-21) and FAPEMIG/Brazil (CEX APQ 04528/22)Subjects: Analysis of PDEs (math.AP); Functional Analysis (math.FA)
We investigated the existence of solutions for a class of Ambrosetti-Prodi type systems involving the fractional Laplacian operator and with nonlinearities reaching critical growth and interacting, in some sense, with the spectrum of the operator. The resonant case in $\lambda_{k,s}$ for $k>1$ is also investigated.
- [13] arXiv:2405.04302 [pdf, ps, other]
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Title: On the existence and uniqueness of weak solutions to elliptic equations with a singular driftComments: arXiv admin note: text overlap with arXiv:2208.10909Subjects: Analysis of PDEs (math.AP)
In this paper we study the Dirichlet problem for a scalar elliptic equation in a bounded Lipschitz domain $\Omega \subset \mathbb R^3$ with a singular drift of the form $b_0= b-\alpha \frac {x'}{|x'|^2}$ where $x'=(x_1,x_2,0)$, $\alpha \in \mathbb R$ is a parameter and $b$ is a divergence free vector field having essentially the same regularity as the potential part of the drift. Such drifts naturally arise in the theory of axially symmetric solutions to the Navier-Stokes equations. For $\alpha <0$ the divergence of such drifts is positive which potentially can ruin the uniqueness of solutions. Nevertheless, for $\alpha<0$ we prove existence and H\"older continuity of a unique weak solution which vanishes on the axis $\Gamma:=\{ ~x\in \mathbb R^3:~|x'|=0~\}$.
- [14] arXiv:2405.04310 [pdf, ps, other]
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Title: Time-asymptotics of a heated stringSubjects: Analysis of PDEs (math.AP)
In the present paper, we study a model of a thermoelastic string that is initially heated. We classify all the possible asymptotic states when time tends to infinity of such a model. Actually, we show that whatever the initial data is, a heated string must converge to a flat, steady string with uniformly distributed heat. The latter distribution is calculated from the energy conservation. In order to obtain the result, we need to take a few steps. In the first two steps, time-independent bounds from above and from below (by a positive constant) of the temperature are obtained. This is done via the Moser-like iteration. The lower bound is obtained via the Moser iteration on the negative part of the logarithm of temperature. In the third step, we obtain a time-independent higher-order estimate, which yields compactness of a sequence of the values of the solution when time tends to infinity. Here, an estimate involving the Fisher information of temperature, together with a recent functional inequality from \cite{CFHS} and an $L^2(L^2)$ estimate of the gradient of entropy, enable us to arrive at a tricky Gr\"{o}nwall type inequality. Finally, in the last steps, we define the dynamical system on a proper functional phase space and study its $\omega$-limit set. To this end, we use, in particular, the quantitative version of the second principle of thermodynamics. Also, the entropy dissipation term and the bound of the entropy from below are useful when identifying the structure of the $\omega$-limit set.
- [15] arXiv:2405.04320 [pdf, other]
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Title: Stress solution of static linear elasticity with mixed boundary conditions via adjoint linear operatorsSubjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Functional Analysis (math.FA)
We revisit stress problems in linear elasticity to provide a perspective from the geometrical and functionalanalytic points of view. For the static stress problem of linear elasticity with mixed boundary conditions we write the associated pair of unbounded adjoint operators. The stress solution is found as an intersection of affine translations of the fundamental subspaces of the adjoint operators. In particular, we treat the equilibrium equation in the operator form, involving spaces of traces on a part of the boundary, known as Lions-Magenes spaces. Our analysis of the pair of adjoint operators for the problem with mixed boundary conditions relies on the properties of the analogous pair of operators for the problem with the displacement boundary conditions, which we also include in the paper.
- [16] arXiv:2405.04348 [pdf, other]
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Title: Overdetermined elliptic problems in nontrivial exterior domains of the hyperbolic spaceComments: 26 pagesSubjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
We construct nontrivial unbounded domains $\Omega$ in the hyperbolic space $\mathbb{H}^N$, $N \in \{2,3,4\}$, bifurcating from the complement of a ball, such that the overdetermined elliptic problem \begin{equation} -\Delta_{\mathbb{H}^N} u+u-u^p=0\,\, \text{in}\,\,\Omega, \,\, u=0,\,\,\partial_\nu u=\text{const}\,\,\text{on}\,\,\partial\Omega\nonumber \end{equation} has a positive bounded solution in $C^{2,\alpha}\left(\Omega\right) \cap H^1\left(\Omega\right)$. We also give a condition under which this construction holds for larger dimensions $N$. This is linked to the Berestycki-Caffarelli-Nirenberg conjecture on overdetermined elliptic problems, and, as far as we know, is the first nontrivial example of solution to an overdetermined elliptic problem in the hyperbolic space.
- [17] arXiv:2405.04388 [pdf, ps, other]
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Title: Boundary unique continuation in planar domains by conformal mappingAuthors: Stefano VitaComments: 11 pages, comments are welcomeSubjects: Analysis of PDEs (math.AP)
Let $\Omega\subset\mathbb R^2$ be a chord arc domain with small constant. We show that a nontrivial harmonic function which vanishes continuously on a relatively open set of the boundary cannot have the norm of the gradient which vanishes on a subset of positive surface measure (arc length). This result was previously known to be true, and conjectured in higher dimensions by Lin, in Lipschitz domains. Let now $\Omega\subset\mathbb R^2$ be a $C^1$ domain with Dini mean oscillations. We prove that a nontrivial harmonic function which vanishes continuously on a relatively open subset of the boundary $\partial\Omega\cap B_1$ has a finite number of critical points in $\overline\Omega\cap B_{1/2}$. The latter improves some recent results by Kenig and Zhao. Our technique involves a conformal mapping which moves the boundary where the harmonic function vanishes into an interior nodal line of a new harmonic function, after a further reflection. Then, size estimates of the critical set - up to the boundary - of the original harmonic function can be understood in terms of estimates of the interior critical set of the new harmonic function and of the critical set - up to the boundary - of the conformal mapping.
- [18] arXiv:2405.04449 [pdf, ps, other]
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Title: Derivation of kinetic and diffusion equations from a hard-sphere Rayleigh gas using collision trees and semigroupsComments: To appear in LMS lecture notes for conference 'Dynamics, Bifurcations and Numerics', University of Surrey, July 2023Subjects: Analysis of PDEs (math.AP); Dynamical Systems (math.DS)
We will revisit the classical questions of understanding the statistics of various deterministic dynamics of $N$ hard spheres of diameter $\varepsilon$ with random initial data in the Boltzmann-Grad scaling as $\varepsilon$ tends to zero and $N$ tends to infinity. The convergence of the empiric particle dynamics to the Boltzmann-type dynamics is shown using semigroup methods to describe probability measures on collision trees associated to physical trajectories in the case of a Rayleigh gas. As an application we derive the diffusion equation by a further rescaling.
- [19] arXiv:2405.04473 [pdf, ps, other]
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Title: Nonlinear Landau damping and wave operators in sharp Gevrey spacesComments: 38 pagesSubjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
We prove nonlinear Landau damping in optimal weighted Gevrey-3 spaces for solutions of the confined Vlasov-Poisson system on $\T^d\times\R^d$ which are small perturbations of homogeneous Penrose-stable equilibria.
We also prove the existence of nonlinear scattering operators associated to the confined Vlasov-Poisson evolution, as well as suitable injectivity properties and Lipschitz estimates (also in weighted Gevrey-3 spaces) on these operators.
Our results give definitive answers to two well-known open problems in the field, both of them stated in the recent review of Bedrossian [4, Section 6]. - [20] arXiv:2405.04482 [pdf, ps, other]
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Title: Harnack inequality for parabolic equations in double-divergence form with singular lower order coefficientsComments: 18 pagesSubjects: Analysis of PDEs (math.AP); Probability (math.PR)
This paper investigates the Harnack inequality for nonnegative solutions to second-order parabolic equations in double divergence form. We impose conditions where the principal coefficients satisfy the Dini mean oscillation condition in $x$, while the drift and zeroth-order coefficients belong to specific Morrey classes. Our analysis contributes to advancing the theoretical foundations of parabolic equations in double divergence form, including Fokker-Planck-Kolmogorov equations for probability densities.
Cross-lists for Wed, 8 May 24
- [21] arXiv:2405.04112 (cross-list from physics.flu-dyn) [pdf, other]
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Title: Logarithmic lattice models for flows with boundariesComments: 37 pages, 13 figuresSubjects: Fluid Dynamics (physics.flu-dyn); Analysis of PDEs (math.AP)
Many fundamental problems in fluid dynamics are related to the effects of solid boundaries. In general, they install sharp gradients and contribute to the developement of small-scale structures, which are computationally expensive to resolve with numerical simulations. A way to access extremely fine scales with a reduced number of degrees of freedom is to consider the equations on logarithmic lattices in Fourier space. Here we introduce new toy models for flows with walls, by showing how to add boundaries to the logarithmic lattice framework. The resulting equations retain many important properties of the original systems, such as the conserved quantities, the symmetries and the boundary effects. We apply this technique to many flows, with emphasis on the inviscid limit of the Navier-Stokes equations. For this setup, simulations reach impressively large Reynolds numbers and disclose interesting insights about the original problem.
- [22] arXiv:2405.04208 (cross-list from math.DG) [pdf, ps, other]
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Title: Collapsing immortal Kähler-Ricci flowsComments: 89 pagesSubjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP)
We consider the K\"ahler-Ricci flow on compact K\"ahler manifolds with semiample canonical bundle and intermediate Kodaira dimension, and show that the flow collapses to a canonical metric on the base of the Iitaka fibration in the locally smooth topology and with bounded Ricci curvature away from the singular fibers. This follows from an asymptotic expansion for the evolving metrics, in the spirit of recent work of the first and third-named authors on collapsing Calabi-Yau metrics, and proves two conjectures of Song and Tian.
- [23] arXiv:2405.04220 (cross-list from math.CA) [pdf, ps, other]
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Title: A characterization of wavelet sets on Vilenkin groups with its application to construction of MRA waveletsComments: 28 pagesSubjects: Classical Analysis and ODEs (math.CA); Analysis of PDEs (math.AP); Functional Analysis (math.FA)
Let $G$ be a Vilenkin group. In 2008, Y. A. Farkov constructed wavelets on $G$ via the multiresolution analysis method. In this article, a characterization of wavelet sets on $G$ is established, which provides another method for the construction of wavelets. As an application, the relation between multiresolution analyses and wavelets determined from wavelet sets is also presented. To some extent, these results positively answer a question mentioned by P. Mahapatra and D. Singh in [Bull. Sci. Math. 167 (2021), Paper No. 102945, 20 pp].
- [24] arXiv:2405.04301 (cross-list from math.DG) [pdf, ps, other]
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Title: Classification of solutions to the isotropic horospherical $p$-Minkowski problem in hyperbolic planeComments: 19 pages, 2 figures. All comments are welcomeSubjects: Differential Geometry (math.DG); Analysis of PDEs (math.AP); Metric Geometry (math.MG)
In \cite{LX}, the first author and Xu introduced and studied the horospherical $p$-Minkowski problem in hyperbolic space $\mathbb{H}^{n+1}$. In particular, they established the uniqueness result for solutions to this problem when the prescribed function is constant and $p\ge -n$. This paper focuses on the isotropic horospherical $p$-Minkowski problem in hyperbolic plane $\mathbb{H}^{2}$, which corresponds to the equation \begin{equation}\label{0}
\varphi^{-p}\left(\varphi_{\theta\theta}-\frac{\varphi_{\theta}^2}{2\varphi}+\frac{\varphi-\varphi^{-1}}{2}\right)=\gamma\quad\text{on}\ \mathbb{S}^1, \end{equation} where $\gamma$ is a positive constant. We provide a classification of solutions to the above equation for $p\ge -7$, as well as a nonuniqueness result of solutions for $p<-7$. Furthermore, we extend this problem to the isotropic horospherical $q$-weighted $p$-Minkowski problem in hyperbolic plane and derive some uniqueness and nonuniqueness results. - [25] arXiv:2405.04384 (cross-list from math.CV) [pdf, ps, other]
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Title: Geodesic connectivity and rooftop envelopes in the Cegrell classesSubjects: Complex Variables (math.CV); Analysis of PDEs (math.AP); Differential Geometry (math.DG)
This study examines geodesics and plurisubharmonic envelopes within the Cegrell classes on bounded hyperconvex domains in $\mathbb{C}^n$. We establish that solutions possessing comparable singularities to the complex Monge-Amp\`ere equation are identical, affirmatively addressing a longstanding open question raised by Cegrell. This achievement furnishes the most general form of the Bedford-Taylor comparison principle within the Cegrell classes. Building on this foundational result, we explore plurisubharmonic geodesics, broadening the criteria for geodesic connectivity among plurisubharmonic functions with connectable boundary values. Our investigation also delves into the notion of rooftop envelopes, revealing that the rooftop equality condition and the idempotency conjecture are valid under substantially weaker conditions than previously established, a finding made possible by our proven uniqueness result. The paper concludes by discussing the core open problems within the Cegrell classes related to the complex Monge-Amp\`ere equation.
Replacements for Wed, 8 May 24
- [26] arXiv:2008.13728 (replaced) [pdf, other]
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Title: Dynamical instability of minimal surfaces at flat singular pointsComments: 31 pages, 3 figures. In v2 we discuss more extensively the range of applicability of our result in the context of the state of the art on the analysis of branched minimal surfaces. This is the final version, to appear on the Journal of Differential GeometrySubjects: Analysis of PDEs (math.AP); Differential Geometry (math.DG)
- [27] arXiv:2108.13668 (replaced) [pdf, other]
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Title: A globally stable self-similar blowup profile in energy supercritical Yang-Mills theoryComments: 57 pages, 5 figures, with minor improvements to match the published versionJournal-ref: Comm. Partial Differential Equations 48 (2023), no. 9, 1148-1213Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
- [28] arXiv:2302.01832 (replaced) [pdf, ps, other]
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Title: Remarks on hypoelliptic equationsComments: Revised versionSubjects: Analysis of PDEs (math.AP)
- [29] arXiv:2304.08187 (replaced) [pdf, ps, other]
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Title: Stable blowup for focusing semilinear wave equations in all dimensionsAuthors: Matthias OstermannComments: 45 pages, with minor improvements to match the published versionSubjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph)
- [30] arXiv:2306.08437 (replaced) [pdf, ps, other]
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Title: Nonlinear asymptotic mean value characterizations of holomorphic functionsComments: 25 pagesSubjects: Analysis of PDEs (math.AP); Complex Variables (math.CV)
- [31] arXiv:2309.08364 (replaced) [pdf, ps, other]
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Title: On some isoperimetric inequalities for the Newtonian capacityAuthors: Michiel van den BergComments: 15 pagesSubjects: Analysis of PDEs (math.AP)
- [32] arXiv:2310.17702 (replaced) [pdf, ps, other]
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Title: Existence of global weak solutions to NSE in weighted spacesAuthors: Misha ChernobaiSubjects: Analysis of PDEs (math.AP)
- [33] arXiv:2311.09949 (replaced) [pdf, ps, other]
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Title: Cluster semiclassical states of the nonlinear Schrödinger-Bopp-Podolsky systemAuthors: Gustavo de Paula RamosComments: 24 pages; major revision and different main result; comments are welcomeSubjects: Analysis of PDEs (math.AP)
- [34] arXiv:2312.00606 (replaced) [pdf, other]
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Title: The continuum limit of non-local Follow-the-Leader modelsComments: Changed to periodic boundary conditionsSubjects: Analysis of PDEs (math.AP)
- [35] arXiv:2401.04969 (replaced) [pdf, ps, other]
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Title: Pointwise estimates for the fundamental solution of higher order Schrödinger equation in odd dimensionsComments: Full details for the high energy part presented, 101ppSubjects: Analysis of PDEs (math.AP)
- [36] arXiv:2401.15959 (replaced) [pdf, ps, other]
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Title: Existence and regularity for a $p$-Laplacian problem in $\mathbb{R}^N$ with singular, convective, critical reactionSubjects: Analysis of PDEs (math.AP)
- [37] arXiv:2404.15205 (replaced) [pdf, ps, other]
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Title: Heat flow, log-concavity, and Lipschitz transport mapsSubjects: Analysis of PDEs (math.AP); Probability (math.PR)
- [38] arXiv:2405.01982 (replaced) [pdf, ps, other]
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Title: Global regularity for solutions of magnetohydrodynamic equations with large initial dataAuthors: Xiangsheng XuComments: arXiv admin note: substantial text overlap with arXiv:2404.16433Subjects: Analysis of PDEs (math.AP)
- [39] arXiv:2405.03214 (replaced) [pdf, ps, other]
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Title: Asymptotic behavior toward viscous shock for impermeable wall and inflow problem of barotropic Navier-Stokes equationsSubjects: Analysis of PDEs (math.AP)
- [40] arXiv:2405.03407 (replaced) [pdf, ps, other]
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Title: $k$-convex hypersurfaces with prescribed Weingarten curvature in warped product manifoldsComments: 19 pages. arXiv admin note: substantial text overlap with arXiv:2105.12047Subjects: Analysis of PDEs (math.AP)
- [41] arXiv:2209.02286 (replaced) [pdf, ps, other]
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Title: A characterization of the subspace of radially symmetric functions in Sobolev spacesAuthors: Matthias OstermannComments: 12 pages, revised and restructured to match the published version. Section 1 and 2 have been expanded and improved, Theorem 1 in v1 has been split into Theorems 1.1 and 1.2, an application to Sobolev norms of corotational maps has been added in Theorem 1.3, references have been updatedSubjects: Functional Analysis (math.FA); Mathematical Physics (math-ph); Analysis of PDEs (math.AP)
- [42] arXiv:2212.04083 (replaced) [pdf, ps, other]
- [43] arXiv:2312.15126 (replaced) [pdf, ps, other]
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Title: The Dirac Delta as a Singular Potential for the 2D Schrodinger EquationAuthors: Michael MarounComments: 10 pagesSubjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Functional Analysis (math.FA); Spectral Theory (math.SP)
- [44] arXiv:2312.17712 (replaced) [pdf, ps, other]
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Title: The Euclidean-hyperboloidal foliation method. Application to f(R) modified gravityComments: 46 pagesSubjects: General Relativity and Quantum Cosmology (gr-qc); Analysis of PDEs (math.AP)
- [45] arXiv:2402.07060 (replaced) [pdf, other]
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Title: Spectral convergence of a semi-discretized numerical system for the spatially homogeneous Boltzmann equation with uncertaintiesComments: Revised version. To appear in SIAM/ASA Journal on Uncertainty QuantificationSubjects: Numerical Analysis (math.NA); Analysis of PDEs (math.AP)
- [46] arXiv:2405.03238 (replaced) [pdf, other]
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Title: Interface Modes in Honeycomb Topological Photonic Structures with Broken Reflection SymmetrySubjects: Mathematical Physics (math-ph); Analysis of PDEs (math.AP); Spectral Theory (math.SP); Optics (physics.optics)
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