Calculus of Variations and Geometric Measure Theory

S. Dweik

$L^{p,q}$ estimates on the transport density

created by dweik on 21 Mar 2019


Accepted Paper

Inserted: 21 mar 2019
Last Updated: 21 mar 2019

Journal: Communications on Pure and Applied Analysis
Year: 2019


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).

Keywords: Monge-Kantorovich problem, Transport density, Lorentz regularity