EIGENVALUES OF THE FINSLER p ‐LAPLACIAN ON VARYING DOMAINS
| Autor: | Giuseppina di Blasio, Pier Domenico Lamberti |
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| Přispěvatelé: | DI BLASIO, Giuseppina, Domenico Lamberti, Pier |
| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
General Mathematics Mathematics::Spectral Theory Eigenfunction Domain (mathematical analysis) 35P15 35J25 47A75 47B25 domain perturbation Mathematics - Spectral Theory Overdetermined system Identity (mathematics) Mathematics - Analysis of PDEs Hadamard transform FOS: Mathematics p-Laplacian Differentiable function Finsler anisotropic p-Laplacian stability of eigenvalues domain perturbation Spectral Theory (math.SP) anisotropic p-Laplacian Eigenvalues and eigenvectors Analysis of PDEs (math.AP) Finsler stability of eigenvalues Mathematics |
| Zdroj: | Mathematika. 66:765-776 |
| ISSN: | 2041-7942 0025-5793 |
| DOI: | 10.1112/mtk.12042 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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