Generalized Pohozaev identity and a non-existence result for the p-Laplacian: weak solutions

Abstract

In this paper, a generalization of the well-known Pohožaev identity and a non-existence result for some Dirichlet problems with the p-Laplacian are obtained. As a preliminary, we will give some necessary technical results regarding the differential calculus in Sobolev spaces and the differentiability properties of superposition operators between Sobolev spaces (in the Marcus-Mizel direction).