We consider the minimization problem for an integral functional $J$, possibly nonconvex and noncoercive in $W^{1,1}_0(\Omega)$, where $\Omega\subset\R^n$ 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 solution of a system of PDEs of Monge-Kantorovich type arising in problems of mass transfer theory.
A sharp uniqueness result for a class of variational problems solved by a distance function / Crasta, Graziano; Malusa, Annalisa. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - STAMPA. - 243:2(2007), pp. 427-447. [10.1016/j.jde.2007.05.026]
A sharp uniqueness result for a class of variational problems solved by a distance function
CRASTA, Graziano;MALUSA, ANNALISA
2007
Abstract
We consider the minimization problem for an integral functional $J$, possibly nonconvex and noncoercive in $W^{1,1}_0(\Omega)$, where $\Omega\subset\R^n$ 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 solution of a system of PDEs of Monge-Kantorovich type arising in problems of mass transfer theory.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
