Pohozaev identities for weak solutions of Grushin type p-sub-Laplacian equation via domain variations

Abstract

In this paper, we study Pohozaev identities for weak solutions of degenerate elliptic equations involving Grushin type p-sub-Laplacian under only $C^1$-regularity assumption. By using domain variations, we obtain the local Pohozaev identities of translating type and scaling type. As an application, a global Pohozaev identity of scaling type in ${\mathbb{R}}^{N+l}$ is also derived.