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 is greater than 0, and some other families of domains where it is equal to 0. We also give a new result on "trap domains" defined in [BCM], i.e., domains where reflecting Brownian motion takes a long time to reach the center of the domain.