Super and Weak Poincar\'e Inequalities for Sticky-Reflected Diffusion Processes

TL;DR

This paper extends the study of Poincaré inequalities to more general sticky-reflected diffusion processes, providing new theoretical results on their convergence and integrability properties with practical examples.

Contribution

It introduces super and weak Poincaré inequalities for a broader class of sticky-reflected diffusions, advancing understanding beyond previous Brownian motion cases.

Findings

Established super and weak Poincaré inequalities for general sticky-reflected diffusions.

Characterized convergence rates of associated diffusion semigroups.

Provided concrete examples illustrating the main results.

Abstract

As a continuation to \cite{MRW} where the Poincar\'e and log-Sobolev inequalities were studied for the sticky-reflected Brownian motion on Riemannian manifolds with boundary, this paper establishes the super and weak Poincar\'e 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.