A sharp uniqueness result for a class of variational problems solved by a distance function

[摘要] We consider the minimization problem for an integral functional J, possibly nonconvex and noncoercive in W-0(1,1) (Omega), where Omega subset of R-n 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. (C) 2007 Elsevier Inc. All rights reserved.

[发布日期] 2007-12-15

[关键词] minimum problems with constraints;uniqueness;enter equation;distance function;mass transfer problems;p-Laplace equation