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On the Robin problem in fractal domains

2007; Wiley; Volume: 96; Issue: 2 Linguagem: Inglês

10.1112/plms/pdm045

1460-244X

Richard F. Bass, Krzysztof Burdzy, Zhen-Qing Chen,

Analytic and geometric function theory

Proceedings of the London Mathematical SocietyVolume 96, Issue 2 p. 273-311 Articles On the Robin problem in fractal domains Richard F. Bass, Richard F. Bass bass@math.uconn.edu Department of Mathematics, University of Connecticut, Storrs, CT, 06269-3009 USASearch for more papers by this authorKrzysztof Burdzy, Corresponding Author Krzysztof Burdzy burdzy@math.washington.edu Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350 USAburdzy@math.washington.eduSearch for more papers by this authorZhen-Qing Chen, Zhen-Qing Chen zchen@math.washington.edu Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350 USASearch for more papers by this author Richard F. Bass, Richard F. Bass bass@math.uconn.edu Department of Mathematics, University of Connecticut, Storrs, CT, 06269-3009 USASearch for more papers by this authorKrzysztof Burdzy, Corresponding Author Krzysztof Burdzy burdzy@math.washington.edu Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350 USAburdzy@math.washington.eduSearch for more papers by this authorZhen-Qing Chen, Zhen-Qing Chen zchen@math.washington.edu Department of Mathematics, University of Washington, Box 354350, Seattle, WA, 98195-4350 USASearch for more papers by this author First published: 25 October 2007 https://doi.org/10.1112/plms/pdm045Citations: 17 2000 Mathematics Subject Classification 60H30 (primary) 35J25, 60J65 (secondary). AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat 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. Citing Literature Volume96, Issue2March 2008Pages 273-311 RelatedInformation