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).
