An overdetermined problem for the Helmholtz equation
نویسندگان
چکیده
منابع مشابه
An Overdetermined Problem for an Elliptic Equation
We consider the following overdetermined boundary value problem: ∆u+ λu+ μ = 0 in Ω, u = 0 on ∂Ω and ∂u/∂n = c on ∂Ω, where c 6= 0, λ and μ are real constants and Ω ⊂ R is a smooth bounded convex open set. We first show that it may happen that the problem has no solution. Then we study the existence of solutions for a wide class of domains. 2010 Mathematics Subject Classification: 35J05, 35R30.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2013
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-2013-11867-8