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In this paper, we show a new regularity result on the transport density{\sigma} in the classical Monge-Kantorovich optimal mass transport problembetween two measures, {\mu} and {\nu}, having some summable densities, f^+ andf^-. More precisely, we prove that the transport density {\sigma} belongs toL^{p,q}({\Omega}) as soon as f^+, f^- \in L^{p,q}({\Omega}).

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