Calculus of Variations and Geometric Measure Theory

G. Crasta - A. Malusa

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

created by malusa on 07 Mar 2008


Published Paper

Inserted: 7 mar 2008

Journal: J. Differential Equations
Volume: 243
Pages: 427-447
Year: 2007


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.