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].

MSC:

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

Zbl 1092.31006