Super and Weak Poincaré Inequalities for Sticky-Reflected Diffusion Processes

Abstract

As a continuation to \cite{MRW} where the Poincaré and log-Sobolev inequalities were studied for the sticky-reflected Brownian motion on Riemannian manifolds with boundary, this paper establishes the super and weak Poincaré inequalities for more general sticky-reflected diffusion processes. As applications, the convergence rate and uniform integrability of the associated diffusion semigroups are characterized. The main results are illustrated by concrete examples.