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

被引：6

作者：

Crasta, Graziano ^{[1
]}

Malusa, Annalisa ^{[1
]}

机构：

[1] Univ Rome 1, Dipartimento Matemat G Castelnuovo, I-00185 Rome, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 243卷 / 02期

关键词：

minimum problems with constraints; uniqueness; enter equation; distance function; mass transfer problems; p-Laplace equation;

D O I：

10.1016/j.jde.2007.05.026

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页码：427 / 447

页数：21

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