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
Autores principales: Da Silva, J.V., Rossi, J.D., Salort, A.M.
Formato: JOUR
Materias:
Approximation of domains
∞-eigenvalue problem
∞-eigenvalues estimates
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_10726691_v2018_n_p_DaSilva
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
Descripción
Sumario: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.

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