Super and weak Poincaré inequalities for sticky-reflected diffusion processes

As a continuation to (M. Bormann, M. von Renesse, and F.-Y. Wang, “Functional inequalities for Brownian motion on Riemannian manifolds with sticky-reflecting boundary diffusion,” Probab. Theor. Relat. Fields , vol. 194, nos. 1–2, pp. 205–244, 2026) 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.