A boundary Harnack principle in twisted Hölder domains

Abstract

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 fails. Extensions are given to L-harmonic functions for uniformly elliptic operators L in divergence form.