Stability results for the {Mathematical expression}-dimensional Schiffer conjecture via a perturbation method
Given a eigenvalue {Mathematical expression} of {Mathematical expression} in the unit ball {Mathematical expression}, with Neumann boundary conditions, we prove that there exists a class {Mathematical expression} of {Mathematical expression}-domains, depending on {Mathematical expression}, such that...
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| Formato: | INPR |
| Lenguaje: | English |
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_09442669_v_n_p1_Canuto |
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| Sumario: | Given a eigenvalue {Mathematical expression} of {Mathematical expression} in the unit ball {Mathematical expression}, with Neumann boundary conditions, we prove that there exists a class {Mathematical expression} of {Mathematical expression}-domains, depending on {Mathematical expression}, such that if {Mathematical expression} is a no trivial solution to the following problem {Mathematical expression} in {Mathematical expression} on {Mathematical expression}, and {Mathematical expression}, with {Mathematical expression}, and {Mathematical expression}, then {Mathematical expression} is a ball. Here {Mathematical expression} is a eigenvalue of {Mathematical expression} in {Mathematical expression}, with Neumann boundary conditions. © 2013 Springer-Verlag Berlin Heidelberg. |
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