On the problem of unique continuation for the p-Laplace equation

TL;DR

This paper investigates whether two solutions to the p-Laplace equation can be identical on an open subset, providing partial results on this unique continuation problem for nonlinear PDEs.

Contribution

It offers new partial results addressing the unique continuation property for solutions of the nonlinear p-Laplace equation.

Findings

Partial results on the unique continuation property.

Insights into conditions under which solutions may coincide.

Advances in understanding nonlinear PDE behavior.

Abstract

We study if two different solutions of the $p$-Laplace equation $$\nabla\cdot(|\nabla u|^{p-2}\nabla u)=0,$$ where $1<p<\infty$, can coincide in an open subset of their common domain of definition. We obtain some partial results on this interesting problem.