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arXiv · 1904.00089

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

Samer Dweik
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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^- \in L^{p,q}(Ω).

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Samer Dweik. 2019-03-29. L^{p,q} estimates on the transport density. https://arxiv.org/abs/1904.00089

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