Analogs of the liouville property for harmonic functions on unbounded domains

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University

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

Keywords: Liouville property, harmonic function, boundary behavior.

UDC: 517.5

MSC: 35R30

Received: 02.12.2019
Revised: 02.12.2019
Accepted: 19.02.2020

DOI: 10.33048/smzh.2020.61.403

 English version: Siberian Mathematical Journal, 2020, 61:4, 589–599

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