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

[BibTeX]

Preprint

Inserted: 8 sep 2022
Last Updated: 8 sep 2022

Year: 2022

Abstract:

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


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