Martin kernels of general domains. (English) Zbl 1117.31005

Aikawa, Hiroaki (ed.) et al., Potential theory in Matsue. Selected papers of the international workshop on potential theory, Matsue, Japan, August 23–28, 2004. Tokyo: Mathematical Society of Japan (ISBN 4-931469-33-7/hbk). Advanced Studies in Pure Mathematics 44, 145-154 (2006).
The author summarises results from three of his recent papers, as follows: (1) Theorems concerning John domains which bound the number of minimal Martin boundary points that are associated with a Euclidean boundary point; see H. Aikawa, K. Hirata and T. Lundh [J. Math. Soc. Japan 58, 247–274 (2006; Zbl 1092.31006)]. (2) Results connecting the boundary behaviour of quotients of Martin kernels for two domains with the notion of minimal thinness (from a preprint). (3) Comparison estimates for the Green function and Martin kernel associated with uniform domains (from another preprint).
For the entire collection see [Zbl 1102.31001].


31C35 Martin boundary theory
31B25 Boundary behavior of harmonic functions in higher dimensions


Zbl 1092.31006