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

• Qiaoling Wang ^[1] ; Changyu Xia ^[1]
  1. [1] Universidade de Brasília

     Universidade de Brasília

     Brasil

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 36, Nº 4, 2020, págs. 1257-1278
• Idioma: inglés
• DOI: 10.4171/rmi/1166
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• Resumen

  • 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.