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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Detalles Bibliográficos
Publicado: 2018
Materias:
Approximation of domains
∞-eigenvalue problem
∞-eigenvalues estimates
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2018_n_p_DaSilva
http://hdl.handle.net/20.500.12110/paper_10726691_v2018_n_p_DaSilva
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_10726691_v2018_n_p_DaSilva
record_format dspace
spelling paper:paper_10726691_v2018_n_p_DaSilva2023-06-08T16:04:55Z Uniform stability of the ball with respect to the first dirichlet and neumann ∞-eigenvalues 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. 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2018_n_p_DaSilva 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
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.
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
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10726691_v2018_n_p_DaSilva
http://hdl.handle.net/20.500.12110/paper_10726691_v2018_n_p_DaSilva
_version_ 1768542607801057280

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