Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

The Martin boundary in non-Lipschitz domains


Authors: Richard F. Bass and Krzysztof Burdzy
Journal: Trans. Amer. Math. Soc. 337 (1993), 361-378
MSC: Primary 31C35; Secondary 60J45, 60J50
MathSciNet review: 1100692
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in $ {C^\gamma }$ domains, where

$\displaystyle \gamma (x) = bx\log \log (1/x)/\log \log \log (1/x),$

$ b$ small. A counterexample shows that this result is very nearly sharp.

References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 31C35, 60J45, 60J50

Retrieve articles in all journals with MSC: 31C35, 60J45, 60J50


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1993-1100692-9
PII: S 0002-9947(1993)1100692-9
Keywords: Martin boundary, Martin kernel, harmonic functions, minimal harmonic, divergence form operators, conditioned Brownian motion, $ h$-processes
Article copyright: © Copyright 1993 American Mathematical Society