The Martin boundary in non-Lipschitz domains

Bass, Richard F.; Burdzy, Krzysztof

doi:10.1090/S0002-9947-1993-1100692-9

The Martin boundary in non-Lipschitz domains
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by Richard F. Bass and Krzysztof Burdzy PDF

Trans. Amer. Math. Soc. 337 (1993), 361-378 Request permission

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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