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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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_00494704_v40_n_p1_Canuto |
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todo:paper_00494704_v40_n_p1_Canuto2023-10-03T14:52:41Z Local overdetermined linear elliptic problems in Lipschitz domains with solutions changing sign Canuto, B. Rial, D. 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Canuto, B. Rial, D. 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. |
| format |
JOUR |
| author |
Canuto, B. Rial, D. |
| author_facet |
Canuto, B. Rial, D. |
| author_sort |
Canuto, B. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_00494704_v40_n_p1_Canuto |
| work_keys_str_mv |
AT canutob localoverdeterminedlinearellipticproblemsinlipschitzdomainswithsolutionschangingsign AT riald localoverdeterminedlinearellipticproblemsinlipschitzdomainswithsolutionschangingsign |
| _version_ |
1807324472226611200 |