The Martin boundary in non-Lipschitz domains
Richard F. Bass, Krzysztof Burdzy · Transactions of the American Mathematical Society · 1993
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.