On the Robin problem in fractal domains

Abstract

We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum of the solution is greater than 0, and some other families of domains were it is equal to 0. We also give a new result on `trap domains', i.e., domains where reflecting Brownian motion takes a long time to reach the center of the domain.

References in corpus (1)

• Explicit Construction of the Brownian Self-Transport Operator

Cited by in corpus (11)

• Paradigm shift in diffusion-mediated surface phenomena
• Spectral theory of imperfect diffusion-controlled reactions on heterogeneous catalytic surfaces
• The snapping out Brownian motion
• Probability distribution of the boundary local time of reflected Brownian motion in Euclidean domains
• Fluctuations and correlations in chemical reaction kinetics and population dynamics
• Imperfect Diffusion-Controlled Reactions
• Statistics of boundary encounters by a particle diffusing outside a compact planar domain
• Joint distribution of multiple boundary local times and related first-passage time problems with multiple targets
• A guide to Brownian motion and related stochastic processes
• Skew Brownian diffusions across Koch interfaces
• Boundary behavior of Robin problems in non-smooth domains