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arXiv · 1805.02299

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

Changyu Xia·Qiaoling Wang
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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 $\mathbb{R}^n$. 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 nonexistence result for the solutions of the Laplace equation on closed Riemannian manifolds.

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Changyu Xia, Qiaoling Wang. 2018-05-07. Pohozaev identity for the anisotropic $p$-Laplacian and estimates of torsion function. https://arxiv.org/abs/1805.02299

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