A new proof for the equivalence of weak and viscosity solutions for the $p$-Laplace equation

Petri Juutinen; Vesa Julin

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arXiv · 1104.2197

A new proof for the equivalence of weak and viscosity solutions for the $p$-Laplace equation

Petri Juutinen·Vesa Julin

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Abstract

In this paper, we give a new proof for the fact that the distributional weak solutions and the viscosity solutions of the $p$-Laplace equation $-\diver(\abs{Du}^{p-2}Du)=0$ coincide. Our proof is more direct and transparent than the original one by Juutinen, Lindqvist and Manfredi \cite{jlm}, which relied on the full uniqueness machinery of the theory of viscosity solutions. We establish a similar result also for the solutions of the non-homogeneous version of the $p$-Laplace equation.

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Petri Juutinen, Vesa Julin. 2011-04-12. A new proof for the equivalence of weak and viscosity solutions for the $p$-Laplace equation. https://arxiv.org/abs/1104.2197

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