Quasiconvex relaxation of multidimensional control problems with integrands f(t, ξ, v)
University of Graz, Institute for
Mathematics and Scientific Computing, Heinrichstrasse 36, 8010 Graz, Austria. www.thecitytocome.de; email@example.com
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 The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and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.
Mathematics Subject Classification: 26B05 / 26B25 / 49J20 / 49J45 / 68U10
Key words: Quasiconvex functions with infinite values / lower semicontinuous quasiconvex envelope / multidimensional control problem / relaxation / existence of global minimizers / image registration / polyconvex regularization
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