Positive harmonic functions on comb-like domains
Classical Analysis and ODEs
2010-10-04 v1
Abstract
This paper investigates positive harmonic functions on a domain which contains an infinite cylinder, and whose boundary is contained in the union of parallel hyperplanes. (In the plane its boundary consists of two sets of vertical semi-infinite lines.) It characterizes, in terms of the spacing between the hyperplanes, those domains for which there exist minimal harmonic functions with a certain exponential growth.
Cite
@article{arxiv.1010.0036,
title = {Positive harmonic functions on comb-like domains},
author = {Joanna Pres},
journal= {arXiv preprint arXiv:1010.0036},
year = {2010}
}
Comments
18 pages