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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.