On viscosity and weak solutions for non-homogeneous p-Laplace equations

Abstract

In this manuscript, we study the relation between viscosity and weak solutions for non-homogeneous p-Laplace equations with lower order term depending on $x$, $u$ and $abla u$. More precisely, we prove that any locally bounded viscosity solution constitutes a weak solution, extending results presented in Juutinen, Lindqvist and Manfredi cite{JLM}, and Julin and Juutinen cite{JJ}. Moreover, we provide a converse statement in the full case under extra assumptions on the data.