$C^1$ regularity of orthotropic $p-$harmonic functions in the plane

TL;DR

This paper proves that solutions to the orthotropic p-harmonic equation in two dimensions are continuously differentiable, establishing a regularity result for this class of nonlinear PDEs.

Contribution

It demonstrates the $C^1$ regularity of local weak solutions to the orthotropic p-harmonic equation in the plane, a new regularity result for this type of PDE.

Findings

Local weak solutions are $C^1$ functions in $\,\mathbb{R}^2$.

Establishes regularity for orthotropic p-harmonic equations.

Advances understanding of nonlinear PDE regularity in 2D.

Abstract

We prove that local weak solutions of the orthotropic $p-$harmonic equation in $\mathbb{R}^2$ are $C^1$ functions.