Geodesic
On uniqueness theorems for harmonic functions in a cylinder
Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 341-347

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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 $Q$. 
@article{IM2_1967_1_2_a8,
     author = {V. P. Gromov},
     title = {On uniqueness theorems for harmonic functions in a cylinder},
     journal = {Izvestiya. Mathematics },
     pages = {341--347},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1967},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a8/}
}
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V. P. Gromov. On uniqueness theorems for harmonic functions in a cylinder. Izvestiya. Mathematics , Tome 1 (1967) no. 2, pp. 341-347. http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a8/