References & Citations
Mathematics > Analysis of PDEs
Title: Higher Hölder regularity for a subquadratic nonlocal parabolic equation
(Submitted on 25 Apr 2024)
Abstract: In this paper, we are concerned with the H\"older regularity for solutions of the nonlocal evolutionary equation $$ \partial_t u+(-\Delta_p)^s u = 0. $$ Here, $(-\Delta_p)^s$ is the fractional $p$-Laplacian, $0<s<1$ and $1<p<2$. We establish H\"older regularity with explicit H\"older exponents. We also include the inhomogeneous equation with a bounded inhomogeneity. In some cases, the obtained H\"older exponents are almost sharp. Our results complement the previous results for the superquadratic case when $p\geq 2$.
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