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Sibirskii Matematicheskii Zhurnal, 2020, Volume 61, Number 4, Pages 752–764
DOI: https://doi.org/10.33048/smzh.2020.61.403 (Mi smj6017) 		 
Analogs of the liouville property for harmonic functions on unbounded domains

V. V. Volchkov, Vit. V. Volchkov

Donetsk National University
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DOI: https://doi.org/10.33048/smzh.2020.61.403
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.
Received: 02.12.2019
Revised: 02.12.2019
Accepted: 19.02.2020
English version:
Siberian Mathematical Journal, 2020, Volume 61, Issue 4, Pages 589–599
DOI: https://doi.org/10.1134/S0037446620040035
Bibliographic databases:
Document Type: Article
UDC: 517.5
MSC: 35R30
Language: Russian
Citation: V. V. Volchkov, Vit. V. Volchkov, “Analogs of the liouville property for harmonic functions on unbounded domains”, Sibirsk. Mat. Zh., 61:4 (2020), 752–764; Siberian Math. J., 61:4 (2020), 589–599
Citation in format AMSBIB
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    		Сибирский математический журнал Siberian Mathematical Journal
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