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On uniqueness theorems for harmonic functions in a cylinder

V. P. Gromov


Abstract: Harmonic functions $U(r,\varphi,x)$ in an infinite cylinder $Q$ are considered herein. Conditions are given under which it follows that $U(r,\varphi,x)\equiv0$ from the boundedness of the normal derivative of the function $U(r,\varphi,x)$ on parallel sections of the cylinder $Q$.

UDC: 517.5

MSC: 31C05, 30D20, 35A05, 33C10, 40A05

Received: 16.05.1966

 English version: Mathematics of the USSR-Izvestiya, 1967, 1:2, 341–347

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