Lipschitz Interior regularity for the viscosity and weak solutions of the pseudo-$p$Laplacian

TL;DR

This paper establishes interior Lipschitz regularity for weak and viscosity solutions of the pseudo-$p$Laplacian equation when $p>2$ and the source term is bounded, advancing understanding of solution smoothness.

Contribution

It provides the first interior Lipschitz regularity results for solutions of the pseudo-$p$Laplacian in the specified setting.

Findings

Proves interior Lipschitz regularity for weak solutions.

Establishes interior Lipschitz regularity for viscosity solutions.

Applicable for bounded source term $f$ and $p>2$.

Abstract

We prove interior Lipschitz regularity result for weak and viscosity solutions of the pseudo $p$Laplacien $(p-1)\sum_i |\partial_i u|^{p-2} \partial_{ii} u = f$ for $p>2$ and $f$ bounded.