Calculus of Variations and Geometric Measure Theory

J. B. Casteras - L. Monsaingeon - F. Santambrogio

Sticky-reflecting diffusion as a Wasserstein gradient flow

created by santambro on 31 Jan 2024



Inserted: 31 jan 2024
Last Updated: 31 jan 2024

Year: 2024


In this paper we identify the Fokker-Planck equation for (reflected) Sticky Brownian Motion as a Wasserstein gradient flow in the space of probability measures. The driving functional is the relative entropy with respect to a non-standard reference measure, the sum of an absolutely continuous interior part plus a singular part supported on the boundary. Taking the small time-step limit in a minimizing movement (JKO scheme) we prove existence of weak solutions for the coupled system of PDEs satisfying in addition an Energy Dissipation Inequality.