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A boundary Harnack principle in twisted Hölder domains
(Annals of Mathematics, 1991-09)
The boundary Harnack principle for the ratio of positive harmonic functions is shown to hold in twisted Hölder domains of order [alpha] for [alpha is an element of the set](1/2, 1]. For each [alpha is an element of the set] (0, 1/2), there exists a twisted Hölder domain of order [alpha] for which the boundary Harnack principle ...
The Martin boundary in non-Lipschitz domains
(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 [to the power of 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.