References & Citations
Mathematics > Analysis of PDEs
Title: Interior pointwise regularity for elliptic and parabolic equations in divergence form and applications to nodal sets
(Submitted on 12 May 2024)
Abstract: In this paper, we obtain the interior pointwise $C^{k,\alpha}$ ($k\geq 0$, $0<\alpha<1$) regularity for weak solutions of elliptic and parabolic equations in divergence form. The compactness method and perturbation technique are employed. The pointwise regularity is proved in a very simple way and the results are optimal. In addition, these pointwise regularity can be used to characterize the structure of the nodal sets of solutions.
Link back to: arXiv, form interface, contact.