Equivalence of viscosity and weak solutions for the normalized p(x)-Laplacian

2017/10/21 by Siltakoski, Jarkko
#35D30 #35D40 #35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.07760

Abstract

We show that viscosity solutions to the normalized p(x)-Laplace equation coincide with distributional weak solutions to the strong p(x)-Laplace equation when p is Lipschitz and inf p>1. This yields C^1,α regularity for the viscosity solutions of the normalized p(x)-Laplace equation. As an additional application, we prove a Radó-type removability theorem.

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