Accepted Paper

Inserted: 21 mar 2019
Last Updated: 21 mar 2019

Journal: Communications on Pure and Applied Analysis
Year: 2019

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 L^p,q(Ω) as soon as f^+, f⁻ ∈ L^p,q(Ω).

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

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