On the Local Behavior of Local Weak Solutions to some Singular Anisotropic Elliptic Equations

TL;DR

This paper investigates the local properties of solutions to certain anisotropic singular elliptic equations, establishing regularity and inequalities using a parabolic approach.

Contribution

It introduces a novel parabolic method to analyze the local behavior of solutions to anisotropic singular elliptic equations, including regularity and Harnack inequalities.

Findings

Proves interior Hölder continuity of solutions

Establishes integral and pointwise Harnack inequalities

Develops a parabolic approach for anisotropic singular equations

Abstract

We study the local behavior of bounded local weak solutions to a class of anisotropic singular equations that involves both non-degenerate and singular operators. Throughout a parabolic approach to expansion of positivity we obtain the interior H\"older continuity, and some integral and pointwise Harnack inequalities.