Analogs of the Liouville Property for Harmonic Functions on Unbounded Domains

Сибирский математический журнал

article

V. V. Volchkov¹  V. V. Volchkov¹ 

[1] Donetsk National University

关键词: Liouville property;    harmonic function;    boundary behavior;   

DOI  :  10.1134/S0037446620040035

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We obtain some analogs of the Liouville property for the function that is harmonic on the exterior of a Jordan domain $ G\subset{\mathbb{C}} $ and has constant boundary values of the function itself and its normal derivative. We show that these conditions cannot be relaxed in general.

【 授权许可】

CC BY