Faber-Krahn and Lieb-type inequalities for the composite membrane problem
| Autor: | Giovanni Cupini, Eugenio Vecchi |
|---|---|
| Přispěvatelé: | Cupini G., Vecchi E. |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Composite membrane problem Eigenvalue Faber-Krahn inequality Lieb inequality Rearrangement Inequality Applied Mathematics media_common.quotation_subject 010102 general mathematics General Medicine Mathematics::Spectral Theory 01 natural sciences 010101 applied mathematics Dirichlet eigenvalue Ball (mathematics) Composite membrane 0101 mathematics Laplace operator Analysis Eigenvalues and eigenvectors Mathematics media_common |
| Zdroj: | Communications on Pure & Applied Analysis. 18:2679-2691 |
| ISSN: | 1553-5258 |
| DOI: | 10.3934/cpaa.2019119 |
| Popis: | The classical Faber-Krahn inequality states that, among all domains with given measure, the ball has the smallest first Dirichlet eigenvalue of the Laplacian. Another inequality related to the first eigenvalue of the Laplacian has been proved by Lieb in 1983 and it relates the first Dirichlet eigenvalues of the Laplacian of two different domains with the first Dirichlet eigenvalue of the intersection of translations of them. In this paper we prove the analogue of Faber-Krahn and Lieb inequalities for the composite membrane problem. |
| Databáze: | OpenAIRE |
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