Schauder estimates for parabolic p-Laplace systems

2025/07/21 by Bögelein, Verena, Duzaar, Frank, Gianazza, Ugo +2
#35B45 #35B65 #35K65 #35K67 #35K92 #76S05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2507.15722

Abstract

We establish the local Hölder regularity of the spatial gradient of bounded weak solutions u\colon E_T→\R^k to the non-linear system of parabolic type ∂_tu-\Div( a(x,t)(μ²+|Du|²)^\fracp-22Du)=0 \qquadin E_T, where p>1, μ∈[0,1], and the coefficient a∈ L^∞(E_T) is bounded below by a positive constant and is Hölder continuous in the space variable x. As an application, we prove Hölder estimates for the gradient of weak solutions to a doubly non-linear parabolic equation in the super-critical fast diffusion regime.

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