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

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.

References in corpus (2)

• Strong unique continuation for general elliptic equations in 2D
• The unique continuation property for a nonlinear equation on trees

Cited by in corpus (6)

• The unique continuation property for a nonlinear equation on trees
• The fractional $p$-biharmonic systems: optimal Poincaré constants, unique continuation and inverse problems
• Inverse problems for $p$-Laplace type equations under monotonicity assumptions
• On a frequency function approach to the unique continuation principle
• Quantitative uniqueness estimates for $p$-Laplace type equations in the plane
• A geometric approach to regularity for nonlinear free boundary problems with finite Morse index