A sharp uniqueness result for a class of variational problems solved by a distance function |
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Authors: | Graziano Crasta Annalisa Malusa |
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Institution: | aDipartimento di Matematica “G. Castelnuovo”, Università di Roma I, P.le A. Moro 2, 00185 Roma, Italy |
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Abstract: | We consider the minimization problem for an integral functional J, possibly nonconvex and noncoercive in , where is a bounded smooth set. We prove sufficient conditions in order to guarantee that a suitable Minkowski distance is a minimizer of J. The main result is a necessary and sufficient condition in order to have the uniqueness of the minimizer. We show some application to the uniqueness of the solution of a system of PDEs of Monge–Kantorovich type arising in problems of mass transfer theory. |
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Keywords: | Minimum problems with constraints Uniqueness Euler equation Distance function Mass transfer problems p-Laplace equation |
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