Affiliation:
1. Graduate School of Mathematical Sciences , The University of Tokyo , 3-8-1 Komaba Meguro-ku Tokyo 153-8914 , Japan
Abstract
Abstract
In this paper we consider a very singular elliptic equation that involves an anisotropic diffusion operator, including the one-Laplacian, and is perturbed by a p-Laplacian-type diffusion operator with
1
<
p
<
∞
{1<p<\infty}
. This equation seems analytically difficult to handle near a facet, the place where the gradient vanishes. Our main purpose is to prove that weak solutions are continuously differentiable even across the facet. Here it is of interest to know whether a gradient is continuous when it is truncated near a facet. To answer this affirmatively, we consider an approximation problem, and use standard methods including De Giorgi’s truncation and freezing coefficient methods.
Funder
Japan Society for the Promotion of Science
Subject
Applied Mathematics,Analysis
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