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MiS Preprint

Functional Inequalities for Brownian Motion on Riemannian Manifolds with Sticky-Reflecting Boundary Diffusion

Marie-Christin Bormann, Max von Renesse and Feng-Yu Wang


We prove geometric upper bounds for the Poincar\'{e} and Logarithmic Sobolev constants for Brownian motion on manifolds with sticky reflecting boundary diffusion i.e. extended Wentzell-type boundary condition under general curvature assumptions on the manifold and its boundary. The method is based on an interpolation involving energy interactions between the boundary and the interior of the manifold. As side results we obtain explicit geometric bounds on the first nontrivial Steklov eigenvalue, for the norm of the boundary trace operator on Sobolev functions, and on the boundary trace logarithmic Sobolev constant. The case of Brownian motion with pure sticky reflection is also treated.

MSC Codes:
60J65, 35A23, 58C40

Related publications

2023 Repository Open Access
Marie Bormann, Max von Renesse and Feng-Yu Wang

Functional inequalities for Brownian motion on Riemannian manifolds with sticky-reflecting boundary diffusion