Abstract
We consider different notions of solutions to the p(x)-Laplace equation−div(|Du(x)|p(x)−2Du(x))=0 with 1<p(x)<∞. We show by proving a comparison principle that viscosity supersolutions and p(x)-superharmonic functions of nonlinear potential theory coincide. This implies that weak and viscosity solutions are the same class of functions, and that viscosity solutions to Dirichlet problems are unique. As an application, we prove a Radó type removability theorem.
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More From: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
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