The Pohozaev identity for the anisotropic $p$-Laplacian and estimates of the torsion function
Qiaoling Wang, Changyu Xia · Revista Matemática Iberoamericana · 2020
In this paper we prove a Pohozaev identity for the weighted anisotropic p -Laplace operator. As an application of the identity, we deduce the nonexistence of nontrivial solutions of the Dirichlet problem for the weighted anisotropic p -Laplacian in star-shaped domains of \mathbb R^n . We also provide an upper bound estimate for the first Dirichet eigenvalue of the anisotropic p -Laplacian on bounded domains of \mathbb R^n , some sharp estimates for the torsion function of compact manifolds with boundary and a non-existence result for the solutions of the Laplace equation on closed Riemannian manifolds.