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Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)

Published online by Cambridge University Press:  31 March 2010

Marcus Wagner*
Affiliation:
University of Graz, Institute for Mathematics and Scientific Computing, Heinrichstrasse 36, 8010 Graz, Austria. www.thecitytocome.de; marcus.wagner@uni-graz.at
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Abstract

We prove a general relaxation theorem for multidimensional control problems of Dieudonné-Rashevsky type with nonconvex integrands f(t, ξ, v) in presence of a convex control restriction. The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and admits a global minimizer. As an application, we provide existence theorems for the image registration problem with convex and polyconvex regularization terms.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2010

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