Results
Title

L<sup>p,q</sup> estimates on the transport density.

Authors

Dweik, Samer

Abstract

In this paper, we show a new regularity result on the transport density σ in the classical Monge-Kantorovich optimal mass transport problem between two measures, μ and ν, having some summable densities, f and f−. More precisely, we prove that the transport density σ belongs to Lp,q(Ω) as soon as f ,f− ∈ Lp,q(Ω).

Subjects

DENSITY; ESTIMATES; TRANSPORTATION

Publication

Communications on Pure & Applied Analysis, 2019, Vol 18, Issue 6, p3001

ISSN

1534-0392

Publication type

Academic Journal

DOI

10.3934/cpaa.2019134