Equivalence of Viscosity and Weak Solutions for the $p(x)$-Laplacian

Petri Juutinen, Teemu Lukkari, Mikko Parviainen

We consider different notions of solutions to the $p(x)$-Laplace equation $-÷(\abs{Du(x)}^{p(x)-2}Du(x))=0$ with $1<p(x)<\infty$. We show by proving a comparison principle that vi…