Calculus of Variations and Geometric Measure Theory

G. Buttazzo - E. Stepanov

On regularity of transport density in the Monge-Kantorovich problem

created by buttazzo on 12 Oct 2017


Published Paper

Inserted: 12 oct 2017

Journal: SIAM J. Control Optim.
Volume: 42
Number: 3
Pages: 1044-1055
Year: 2003
Doi: 10.1137/S036301290138568X
Links: paper at the journal web site


We show that the optimal regularity result for the transport density in the classical Monge-Kantorovich optimal mass transport problem, with the measures having summable densities, is a Sobolev differentiability along transport rays.

Keywords: regularity, Transport density, Monge–Kantorovich transport problem