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

TL;DR

This paper derives Pohozaev identities for weak solutions of degenerate elliptic equations involving Grushin type p-sub-Laplacian, using domain variations under minimal regularity assumptions, with applications to global identities.

Contribution

It introduces new Pohozaev identities for degenerate elliptic equations with minimal regularity assumptions using domain variation techniques.

Findings

Local Pohozaev identities of translating and scaling types

Global Pohozaev identity in Euclidean space

Applicability to weak solutions with only C^1 regularity

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.