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A Property of Sobolev Spaces and Existence in Optimal Design

A Property of Sobolev Spaces and Existence in Optimal Design 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Property of Sobolev Spaces and Existence in Optimal Design

Tiba,
Applied Mathematics and Optimization , Volume 47 (1) – Dec 19, 2002
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References (13)

Publisher
Springer Journals
Copyright
Copyright © Inc. by 2002 Springer-Verlag New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics, Simulation
ISSN
0095-4616
eISSN
1432-0606
DOI
10.1007/s00245-002-0740-8
Publisher site
See Article on Publisher Site

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.

Journal

Applied Mathematics and Optimization – Springer Journals

Published: Dec 19, 2002

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