L^{p,q} estimates on the transport density
Functional Analysis
2019-04-02 v1
Abstract
In this paper, we show a new regularity result on the transport density {\sigma} in the classical Monge-Kantorovich optimal mass transport problem between two measures, {\mu} and {\nu}, having some summable densities, f^+ and f^-. More precisely, we prove that the transport density {\sigma} belongs to L^{p,q}({\Omega}) as soon as f^+, f^- \in L^{p,q}({\Omega}).
Keywords
Cite
@article{arxiv.1904.00089,
title = {L^{p,q} estimates on the transport density},
author = {Samer Dweik},
journal= {arXiv preprint arXiv:1904.00089},
year = {2019}
}