On the Robin problem in fractal domains

Details On the Robin problem in fractal domains On the Robin problem in fractal domains

2005-04-14

arxiv.org/abs/math/0504297v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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.

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