On the Lipschitz character of orthotropic $p-$harmonic functions

TL;DR

This paper proves that solutions to orthotropic p-harmonic equations are locally Lipschitz continuous across all dimensions and for all p ≥ 2, extending to more degenerate equations with certain Sobolev space conditions.

Contribution

It establishes the Lipschitz regularity of solutions for a broad class of orthotropic p-harmonic equations, including degenerate cases with Sobolev space right-hand sides.

Findings

Solutions are locally Lipschitz for all p ≥ 2 and dimensions.

Regularity extends to degenerate equations with Sobolev space data.

The results unify and generalize previous regularity findings.

Abstract

We prove that local weak solutions of the orthotropic $p-$harmonic equation are locally Lipschitz, for every $p\ge 2$ and in every dimension. More generally, the result holds true for more degenerate equations with orthotropic structure, with right-hand sides in suitable Sobolev spaces.