arXiv subjects

Thibault Caillet

Publications and source records attributed to Thibault Caillet.

4 recordsLinked to original sources

arXiv2026

Generalized Logarithmic Sobolev Inequality by the JKO Scheme

Using a discrete Bakry-{\'E}mery method based on the JKO scheme, relying on the dissipation of entropy and Fisher information along a discrete flow, we establish new generalized logarithmic Sobolev inequality for log-concave measures of the form $e^{-V}$ under strict convexity assumptions on $V$ . We then show how this method recovers some well-known inequalities. This approach can be viewed as interpolating between the Bakry-{\'E}mery method and optimal transport techniques based on geodesic convexity.

math.AP↗

arXiv2024

Doubly nonlinear diffusive PDEs: new existence results via generalized Wasserstein gradient flows

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 EDI formulation of our PDE and prove that under some integrability assumptions on the initial condition the PDE is satisfied in the sense of distributions.

math.AP↗

arXiv2024

Fisher information and continuity estimates for nonlinear but 1-homogeneous diffusive PDEs (via the JKO scheme)

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. As a corollary, we prove that moduli of continuity are conserved across time for the solutions of those PDEs.

math.AP↗

arXiv2022

The five gradients inequality for non quadratic costs

We give a proof of the "five gradients inequality" of Optimal Transportation Theory for general costs of the form $c(x,y)=h(x-y)$ where $h$ is a $C^1$ strictly convex radially symmetric function.

math.AP↗