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

摘要

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 ∇ ⁡ u {nabla u} . More precisely, we prove that any locally bounded viscosity solution constitutes a weak solution, extending results presented in Juutinen, Lindqvist and Manfredi 9, and Julin and Juutinen 6. Moreover, we provide a converse statement in the full case under extra assumptions on the data.