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

2018/05/07 by Changyu Xia, Xia, Changyu, Qiaoling Wang +1 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1805.02299

openalex publication_date 2018/05/07 · openalex created_date 2018/05/17 · openalex updated_date 2026/08/01

Abstract

In this paper we prove the Pohozaev identity for the weighted anisotropic p-Laplace operator. As an application of our 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 nonexistence result for the solutions of the Laplace equation on closed Riemannian manifolds.

Citations

• The Pohozaev Identity for the Fractional Laplacian
• A symmetry problem in potential theory

Cited by

• Pohozaev-type identities for classes of quasilinear elliptic local and nonlocal equations and systems, with applications

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