Published Paper

Inserted: 31 jan 2024
Last Updated: 9 oct 2025

Journal: Journal de Mathématiques Pures et Appliquées
Volume: 199
Year: 2025

Abstract:

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.

Tags: EYAWKAJKOS

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