Work

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

Year: 2024

Type: article

Abstract: We prove geometric upper bounds for the Poincaré 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.

Source: Probability Theory and Related Fields

DOI: 10.1007/s00440-024-01349-2

Authors: Marie Bormann, Max von Renesse, Feng-Yu Wang

Institutions: Max Planck Institute for Mathematics in the Sciences, Leipzig University, Tianjin University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

Funders: National Natural Science Foundation of China, Max-Planck-Institut für Mathematik in den Naturwissenschaften, National Key Research and Development Program of China