Abstract
We prove a general relaxation theorem for multidimensional control problems of Dieudonne-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 The relaxed problem, wherein the integrand f has been replaced by its lower semicontinuous quasiconvex envelope with respect to the gradient variable, possesses the same finite minimal value as the original problem, and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.
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