Remarks on Local Boundedness and Local H\"older Continuity of Local Weak Solutions to Anisotropic $p$-Laplacian Type Equations

TL;DR

This paper proves that locally bounded weak solutions to certain anisotropic p-Laplacian equations are locally H"older continuous and establishes upper bounds for solutions to a broad class of these equations.

Contribution

It demonstrates local H"older continuity for solutions to a specific class of anisotropic p-Laplacian equations and provides homogeneous upper bounds for a general class.

Findings

Weak solutions are locally H"older continuous.

Homogeneous upper bounds are established.

Results apply to a broad class of anisotropic equations.

Abstract

Locally bounded, local weak solutions to a special class of quasilinear, anisotropic, $p$-Laplacian type elliptic equations, are shown to be locally H\"older continuous. Homogeneous local upper bounds are established for local weak solutions to a general class of quasilinear anisotropic equations.