4 papers · 1 filter
Generalized Logarithmic Sobolev Inequality by the JKO Scheme
Thibault Caillet, Fanch Coudreuse
Using a discrete Bakry-{É}mery method based on the JKO scheme, relying on the dissipation of entropy and Fisher information along a discrete flow, we establish new generalized loga…
Fisher information and continuity estimates for nonlinear but 1-homogeneous diffusive PDEs (via the JKO scheme)
Thibault Caillet, Filippo Santambrogio
In this short paper we prove, using the JKO scheme, that quantities such as the Fisher information stay bounded or decrease across time for a family of 1-homogeneous diffusive PDEs…
Doubly nonlinear diffusive PDEs: new existence results via generalized Wasserstein gradient flows
Thibault Caillet, Filippo Santambrogio
We prove an existence result for a large class of PDEs with a nonlinear Wasserstein gradient flow structure. We use the classical theory of Wasserstein gradient flow to derive an E…
The five gradients inequality for non quadratic costs
Thibault Caillet
We give a proof of the "five gradients inequality" of Optimal Transportation Theory for general costs of the form where is a strictly convex radially symm…