Stability results for the N-dimensional Schiffer conjecture via a perturbation method

Given a eigenvalue μ2 0m of -Δ in the unit ball B1, with Neumann boundary conditions, we prove that there exists a class D of C0,1-domains, depending on μ0m, such that if u is a no trivial solution to the following problem Δu + μu = 0 in Ω, u = 0 on ∂Ω, and ∫∂Ω∂nu = 0, with Ω ∈ D, and μ = μ20 m +o(1...

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Autor principal: Canuto, Bruno
Publicado: 2014
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v50_n1-2_p305_Canuto
http://hdl.handle.net/20.500.12110/paper_09442669_v50_n1-2_p305_Canuto
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_09442669_v50_n1-2_p305_Canuto
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spelling paper:paper_09442669_v50_n1-2_p305_Canuto2023-06-08T15:53:47Z Stability results for the N-dimensional Schiffer conjecture via a perturbation method Canuto, Bruno Given a eigenvalue μ2 0m of -Δ in the unit ball B1, with Neumann boundary conditions, we prove that there exists a class D of C0,1-domains, depending on μ0m, such that if u is a no trivial solution to the following problem Δu + μu = 0 in Ω, u = 0 on ∂Ω, and ∫∂Ω∂nu = 0, with Ω ∈ D, and μ = μ20 m +o(1), then μ is a ball. Here μ is a eigenvalue of -Δ in Ω, with Neumann boundary conditions. © 2013 Springer-Verlag Berlin Heidelberg. Fil:Canuto, B. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2014 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v50_n1-2_p305_Canuto http://hdl.handle.net/20.500.12110/paper_09442669_v50_n1-2_p305_Canuto
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description Given a eigenvalue μ2 0m of -Δ in the unit ball B1, with Neumann boundary conditions, we prove that there exists a class D of C0,1-domains, depending on μ0m, such that if u is a no trivial solution to the following problem Δu + μu = 0 in Ω, u = 0 on ∂Ω, and ∫∂Ω∂nu = 0, with Ω ∈ D, and μ = μ20 m +o(1), then μ is a ball. Here μ is a eigenvalue of -Δ in Ω, with Neumann boundary conditions. © 2013 Springer-Verlag Berlin Heidelberg.
author Canuto, Bruno
spellingShingle Canuto, Bruno
Stability results for the N-dimensional Schiffer conjecture via a perturbation method
author_facet Canuto, Bruno
author_sort Canuto, Bruno
title Stability results for the N-dimensional Schiffer conjecture via a perturbation method
title_short Stability results for the N-dimensional Schiffer conjecture via a perturbation method
title_full Stability results for the N-dimensional Schiffer conjecture via a perturbation method
title_fullStr Stability results for the N-dimensional Schiffer conjecture via a perturbation method
title_full_unstemmed Stability results for the N-dimensional Schiffer conjecture via a perturbation method
title_sort stability results for the n-dimensional schiffer conjecture via a perturbation method
publishDate 2014
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09442669_v50_n1-2_p305_Canuto
http://hdl.handle.net/20.500.12110/paper_09442669_v50_n1-2_p305_Canuto
work_keys_str_mv AT canutobruno stabilityresultsforthendimensionalschifferconjectureviaaperturbationmethod
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