Eigenvalues of the Finsler p-Laplacian on varying domains

2019/11/30 by Giuseppina di Blasio, di Blasio, Giuseppina, Pier Domenico Lamberti +1 · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Nonlinear Partial Differential Equations #Advanced Differential Geometry Research

paper · pdf · doi:10.48550/arxiv.1912.00152

Abstract

We study the dependence of the first eigenvalue of the Finsler p-Laplacian and the corresponding eigenfunctions upon perturbation of the domain and we generalize a few results known for the standard p-Laplacian. In particular, we prove a Frechét differentiability result for the eigenvalues, we compute the corresponding Hadamard formulas and we prove a continuity result for the eigenfunctions. Finally, we briefly discuss a well-known overdetermined problem and we show how to deduce the Rellich-Pohozaev identity for the Finsler p-Laplacian from the Hadamard formula.

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• Anisotropic Improved Leray-Trudinger Inequality

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