Preprint
Inserted: 8 sep 2022
Last Updated: 6 may 2023
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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