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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
DOI: https://doi.org/10.1090/S0002-9947-1993-1100692-9
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 \[ \gamma (x) = bx\log \log (1/x)/\log \log \log (1/x),\] $b$ 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, <IMG WIDTH="17" HEIGHT="19" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$h$">-processes
Article copyright: © Copyright 1993 American Mathematical Society