Positive harmonic functions on comb-like domains

Details Positive harmonic functions on comb-like domains Positive harmonic functions on comb-like domains

2010-09-30

arxiv.org/abs/1010.0036v1

Mathematics

Classical Analysis and ODEs

18 pages

Scientific paper

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.

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