Calculus of Variations and Geometric Measure Theory

G. Bouchitté - G. Buttazzo - L. De Pascale

The Monge-Kantorovich problem for distributions and applications

created by depascal on 01 Oct 2008



Inserted: 1 oct 2008

Year: 2008


We study the Kantorovich-Rubinstein transhipment problem when the difference between the source and the target is not anymore a balanced measure but belongs to a suitable subspace of first order distribution. A particular subclass of such distributions will be considered which includes the infinite sums of dipoles $\sum_k(\delta_{p_k}-\delta_{n_k})$ studied by other authors. In spite of this weakened regularity, it is shown that an optimal transport density still exists among nonnegative finite measures. Some geometric properties of the space of distributions considered can be then deduced.

Keywords: optimal transportation, Monge-Kantorovich problem, flat norm, minimal connections