# 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 $\alpha \in (1/2, 1]$. For each $\alpha \in (0, 1/2)$, 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.

Richard F. Bass

Krzysztof Burdzy