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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