Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues
In this note we analyze how perturbations of a ball Br ⊂ ℝn behaves in terms of their first (non-trivial) Neumann and Dirichlet ∞-eigenvalues when a volume constraint Ln(Ω) = Ln(Br) is imposed. Our main result states that Ω is uniformly close to a ball when it has first Neumann and Dirichlet eigenva...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_10726691_v2018_n_p_DaSilva |
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todo:paper_10726691_v2018_n_p_DaSilva2023-10-03T16:02:51Z Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues Da Silva, J.V. Rossi, J.D. Salort, A.M. Approximation of domains ∞-eigenvalue problem ∞-eigenvalues estimates In this note we analyze how perturbations of a ball Br ⊂ ℝn behaves in terms of their first (non-trivial) Neumann and Dirichlet ∞-eigenvalues when a volume constraint Ln(Ω) = Ln(Br) is imposed. Our main result states that Ω is uniformly close to a ball when it has first Neumann and Dirichlet eigenvalues close to the ones for the ball of the same volume Br. In fact, we show that, if (Formula presented) then there are two balls such that (Formula presented) In addition, we obtain a result concerning stability of the Dirichlet ∞-eigenfunctions. © 2018 Texas State University. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_10726691_v2018_n_p_DaSilva |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Approximation of domains ∞-eigenvalue problem ∞-eigenvalues estimates |
| spellingShingle |
Approximation of domains ∞-eigenvalue problem ∞-eigenvalues estimates Da Silva, J.V. Rossi, J.D. Salort, A.M. Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues |
| topic_facet |
Approximation of domains ∞-eigenvalue problem ∞-eigenvalues estimates |
| description |
In this note we analyze how perturbations of a ball Br ⊂ ℝn behaves in terms of their first (non-trivial) Neumann and Dirichlet ∞-eigenvalues when a volume constraint Ln(Ω) = Ln(Br) is imposed. Our main result states that Ω is uniformly close to a ball when it has first Neumann and Dirichlet eigenvalues close to the ones for the ball of the same volume Br. In fact, we show that, if (Formula presented) then there are two balls such that (Formula presented) In addition, we obtain a result concerning stability of the Dirichlet ∞-eigenfunctions. © 2018 Texas State University. |
| format |
JOUR |
| author |
Da Silva, J.V. Rossi, J.D. Salort, A.M. |
| author_facet |
Da Silva, J.V. Rossi, J.D. Salort, A.M. |
| author_sort |
Da Silva, J.V. |
| title |
Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues |
| title_short |
Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues |
| title_full |
Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues |
| title_fullStr |
Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues |
| title_full_unstemmed |
Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues |
| title_sort |
uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues |
| url |
http://hdl.handle.net/20.500.12110/paper_10726691_v2018_n_p_DaSilva |
| work_keys_str_mv |
AT dasilvajv uniformstabilityoftheballwithrespecttothefirstdirichletandneumanneigenvalues AT rossijd uniformstabilityoftheballwithrespecttothefirstdirichletandneumanneigenvalues AT salortam uniformstabilityoftheballwithrespecttothefirstdirichletandneumanneigenvalues |
| _version_ |
1807320921808044032 |