Orateur
Fanch Coundreuse
Description
The Li–Yau and Aronson–Bénilan estimates are classical inequalities in the theory of the porous medium, heat, and fast diffusion equations. In this talk, I will explore how similar inequalities can be obtained at the level of Wasserstein gradient flow discretizations of these equations, namely the so-called JKO scheme. We will see that the Li–Yau estimate, in the strong Hamilton matrix inequality form, can be fully recovered in the torus and the whole space, while a version of the Aronson–Bénilan estimate holds in dimension one or two and in simple domains. This work is based on arxiv.org/abs/2510.09231 and arxiv.org/abs/2604.04169.