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

preprint2014arXivOpen access

Abstract

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

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