Resumen de The Pohozaev identity for the anisotropic p-Laplacian and estimates of the torsion function

Qiaoling Wang, Changyu Xia

• 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 Rn. We also provide an upper bound estimate for the first Dirichet eigenvalue of the anisotropic p-Laplacian on bounded domains of Rn, 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.