A Property of Sobolev Spaces and Existence in Optimal Design |
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Authors: | Tiba |
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Institution: | (1) Institute of Mathematics, Romanian Academy, P.O. Box 1-764, RO-70700 Bucharest, Romania Dan.Tiba@imar.ro, RO |
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Abstract: | Abstract. We prove that for bounded open sets Ω with continuous boundary, Sobolev spaces of type W
0
l,p
(Ω ) are characterized by the zero extension outside of Ω . Combining this with a compactness result for domains of class C, we obtain a general existence theorem for shape optimization problems governed by nonlinear nonhomogenous Dirichlet boundary
value problems of arbitrary order, in arbitrary dimension and with general cost functionals. |
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Keywords: | , Open sets of class C, Stability of Sobolev spaces, Compactness, AMS Classification, 49D37, 65K10, |
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