Abstract
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.
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Volchkov, V.V., Volchkov, V.V. Analogs of the Liouville Property for Harmonic Functions on Unbounded Domains. Sib Math J 61, 589–599 (2020). https://doi.org/10.1134/S0037446620040035
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DOI: https://doi.org/10.1134/S0037446620040035