Martin boundaries of quasi-sectorial domains
The starting point is a paper by \textit{M. C. Cranston} and \textit{T. S. Salisbury} [Ark. Mat. 31, 27-49 (1993; Zbl 0841.31009)] where the authors obtained an integral test for the existence of a maximal number of minimal Martin boundary points at \(0\) for sectorial domains. In this paper an open Greenian set \(D\) in \(\mathbb R^d\) consisting of \(n\) disjoint open connected cones with Lipschitz boundary and a local Kato measure \(\mu\) supported by \(\partial D\) is considered. Assuming that a boundary Harnack principle holds a sufficient integral criterion for the existence of exactly \(n\) minimal Martin boundary points for \(\Delta -\mu\) at \(0\) is given. In some cases, there is a necessary criterion as well.
scientific article; zbMATH DE number 1523585