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Shape optimization for the Neumann problem of the Laplace equation is important for application and also from the numerical point of view. Mathematical analysis of such problem in the half space is not available. In this paper we prove the shape differentiability of solutions in appropriate weighted Sobolev spaces which describe the behavior of solutions at infinity. We will consider two differ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2011
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-2010-10787-6