Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign

We prove that the only domain Ω such that there exists a solution to the following overdetermined problem Δu+ω2u=-1 in Ω, u=0 on ∂Ω, and ∂nu=c on ∂Ω, is the ball B1, independently on the sign of u, if we assume that the boundary ∂Ω is a perturbation (no necessarily regular) of the unit sphere ∂B1 of...

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Detalles Bibliográficos
Publicado: 2008
Materias:
Elliptic equation
Overdetermined boundary value problem
Radial symmetry
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00494704_v40_n_p1_Canuto
http://hdl.handle.net/20.500.12110/paper_00494704_v40_n_p1_Canuto
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling paper:paper_00494704_v40_n_p1_Canuto2023-06-08T15:05:50Z Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign Elliptic equation Overdetermined boundary value problem Radial symmetry We prove that the only domain Ω such that there exists a solution to the following overdetermined problem Δu+ω2u=-1 in Ω, u=0 on ∂Ω, and ∂nu=c on ∂Ω, is the ball B1, independently on the sign of u, if we assume that the boundary ∂Ω is a perturbation (no necessarily regular) of the unit sphere ∂B1 of ℝn. Here ω2 ≠ (λn)n≥1 (the eigenvalues of -Δ in B1 with Dirichlet boundary conditions), and ω ∉ Λ, where Λ is a enumerable set of ℝ+, whose limit points are the values λ1m, for some integer m ≤ 1, λ1m being the mth-zero of the first-order Bessel function I1. © 2009, EUT Edizioni Universita di Trieste. 2008 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00494704_v40_n_p1_Canuto http://hdl.handle.net/20.500.12110/paper_00494704_v40_n_p1_Canuto
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Elliptic equation
Overdetermined boundary value problem
Radial symmetry
spellingShingle Elliptic equation
Overdetermined boundary value problem
Radial symmetry
Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign
topic_facet Elliptic equation
Overdetermined boundary value problem
Radial symmetry
description We prove that the only domain Ω such that there exists a solution to the following overdetermined problem Δu+ω2u=-1 in Ω, u=0 on ∂Ω, and ∂nu=c on ∂Ω, is the ball B1, independently on the sign of u, if we assume that the boundary ∂Ω is a perturbation (no necessarily regular) of the unit sphere ∂B1 of ℝn. Here ω2 ≠ (λn)n≥1 (the eigenvalues of -Δ in B1 with Dirichlet boundary conditions), and ω ∉ Λ, where Λ is a enumerable set of ℝ+, whose limit points are the values λ1m, for some integer m ≤ 1, λ1m being the mth-zero of the first-order Bessel function I1. © 2009, EUT Edizioni Universita di Trieste.
title Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign
title_short Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign
title_full Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign
title_fullStr Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign
title_full_unstemmed Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign
title_sort local overdetermined linear elliptic problems in lipschitz domains with solutions changing sign
publishDate 2008
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00494704_v40_n_p1_Canuto
http://hdl.handle.net/20.500.12110/paper_00494704_v40_n_p1_Canuto
_version_ 1768542307492036608

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