On the Robin problem in fractal domains
Classical Analysis and ODEs
2014-02-26 v1 Probability
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.
Cite
@article{arxiv.math/0504297,
title = {On the Robin problem in fractal domains},
author = {Richard Bass and Krzysztof Burdzy and Zhen-Qing Chen},
journal= {arXiv preprint arXiv:math/0504297},
year = {2014}
}