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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
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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.

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Keywords: Martin boundary, Martin kernel, harmonic functions, minimal harmonic, divergence form operators, conditioned Brownian motion, $ h$-processes
Article copyright: © Copyright 1993 American Mathematical Society

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