EIGENVALUES OF THE FINSLER  p ‐LAPLACIAN ON VARYING DOMAINS | Zendy

di Blasio Giuseppina | Zendy; Lamberti Pier Domenico | Zendy

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EIGENVALUES OF THE FINSLER p ‐LAPLACIAN ON VARYING DOMAINS

Author(s) -

di Blasio Giuseppina,

Lamberti Pier Domenico

Publication year - 2020

Publication title -

mathematika

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.955

H-Index - 29

eISSN - 2041-7942

pISSN - 0025-5793

DOI - 10.1112/mtk.12042

Subject(s) - mathematics , eigenfunction , hadamard transform , eigenvalues and eigenvectors , laplace operator , pure mathematics , overdetermined system , mathematical analysis , perturbation (astronomy) , differentiable function , domain (mathematical analysis) , quantum mechanics , physics

We study the dependence of the first eigenvalue of the Finsler p ‐Laplacian and the corresponding eigenfunctions on 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, compute the corresponding Hadamard formulas and 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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