doi:10.1112/plms/pdm045 On the Robin problem in fractal domains

and Zhen-Qing Chen 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 to the mixed Dirichlet–Robin boundary problem 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 Burdzy, Chen and Marshall (Math. Z.), that is, domains where reflecting Brownian motion takes a long time to reach the center of the domain. 1