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

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{∇ 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.