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arXiv · 1912.00152

Eigenvalues of the Finsler $p$-Laplacian on varying domains

Giuseppina di Blasio·Pier Domenico Lamberti
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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 Frech\'{e}t 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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Giuseppina di Blasio, Pier Domenico Lamberti. 2019-11-30. Eigenvalues of the Finsler $p$-Laplacian on varying domains. https://arxiv.org/abs/1912.00152

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