Calculus of Variations and Geometric Measure Theory

S. Dweik

BV estimates on the transport density with Dirichlet region on the boundary

created by dweik on 08 Sep 2022
modified on 25 Mar 2024


Accepted Paper

Inserted: 8 sep 2022
Last Updated: 25 mar 2024

Journal: Calculus of Variations and Partial Differential Equations
Year: 2022


In this paper, we prove BV regularity on the transport density in the mass transport problem to the boundary in two dimension under certain conditions on the domain, the boundary cost and the mass distribution. Moreover, we show by a counter-example that the smoothness of the mass distribution, the boundary and the boundary cost does not imply that the transport density is $W^{1,p}$, for some $p > 1$.

Keywords: Transport density, Monge-Kantorovich system , Dirichlet region, BV estimates