Inequalities for generalized entropy and optimal transportation
Dario Cordero–Erausquin, Wilfrid Gangbo, Christian Houdré · Contemporary mathematics - American Mathematical Society · 2004
A new concept of Fisher-information is introduced through a cost function. That concept is used to obtain extensions and variants of transport and logarithmic Sobolev inequalities for general entropy functionals and transport costs. Our proofs rely on optimal mass transport from the Monge-Kantorovich theory. They express the convexity of entropy functionals with respect to suitably chosen paths on the set of probability measures.