All Questions

This question was posted previously but has not attracted any responses so I am repharising it in a slightly different language hoping to reach a wider community Let $(X,d)$ be a pointed metric space ...

Let $(X, | \cdot |)$ be a Banach space. I am interested in whether one can extend the definition of the Kullback-Leibler divergence $$ \text{KL}(\mu \ \Vert \ \nu) := \int_{\Omega} \ln\left(\frac{\...

Let $\mu$ be a compactly supported absolutely continuous probability measure. Let $v,u$ be Lipschitz vector fields. For a vector field $w$ recall that $\Phi_t^w$ denotes its flow. A classical estimate ...

In Alfred Galichon's book Optimal Transport Methods in Economics the foollowing result is stated for OT problems on the real line. Theorem 4.3.(i) Assume that $\Phi$ is supermodular. Then the primal ...

My question is motivated by an optimal transportation approach to PDE's and gradient flows in metric spaces (see e.g Otto's geometry of dissipative evolution equations: the porous media equation and ...