HARMONIC LIOUVILLE THEOREM FOR EXTERIOR DOMAINS REVISITED

Mitsuru Nakai (Japan) and Toshimasa Tada (Japan)

Abstract

We give a very simple and also elementary function theoretic proof for each of and also for the equivalence of two Liouville type theorems for harmonic functions defined on exterior domains one of which is obtained jointly by F. Cammaroto and A. Chinnì in 2000 and the other of which is obtained by M. Özdemir in 2003 and both of which are proved in a convexity theoretic method by corresponding authors. These two theorems themselves are also slightly generalized.

Keywords and phrases: harmonic functions, Liouville theorem, exterior domain, Picard principle.