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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| Formato: | JOUR |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_09442669_v50_n1-2_p305_Canuto |
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| Sumario: | 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. |
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