Petri Juutinen, Vesa Julin
Published 2011-04-12Version 1
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.
Equivalence of viscosity and weak solutions for the normalized $p(x)$-Laplacian
A New Proof of the Equivalence of Weak and Viscosity Solutions to the Homogeneous $\texttt{p}(\cdot)$-Laplacian in $\mathbb{R}^n$
On equivalence of entropy and viscosity solutions to degenerate parabolic equations and applications
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