On the Robin problem in fractal domains

Richard F. Bass; Krzysztof Burdzy; Zhen Qing Chen

doi:10.1112/plms/pdm045

On the Robin problem in fractal domains

Richard F. Bass, Krzysztof Burdzy, Zhen Qing Chen

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

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 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.

Original language	English
Pages (from-to)	273-311
Number of pages	39
Journal	Proceedings of the London Mathematical Society
Volume	96
Issue number	2
DOIs	https://doi.org/10.1112/plms/pdm045
Publication status	Published - Mar 2008
Externally published	Yes

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Bass, R. F., Burdzy, K., & Chen, Z. Q. (2008). On the Robin problem in fractal domains. Proceedings of the London Mathematical Society, 96(2), 273-311. https://doi.org/10.1112/plms/pdm045

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On the Robin problem in fractal domains

Abstract

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