On the Robin problem in fractal domains

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.

• Publication year

  2005

• Venue

  Proceedings of the London Mathematical Society

• Publication date

  2005-04-14

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1112/plms/pdm045arXiv math/0504297
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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