Izvestiya. Mathematics, Tome 1 (1967) no. 2, pp. 341-347
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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/
@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},
year = {1967},
volume = {1},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a8/}
}
TY - JOUR
AU - V. P. Gromov
TI - On uniqueness theorems for harmonic functions in a cylinder
JO - Izvestiya. Mathematics
PY - 1967
SP - 341
EP - 347
VL - 1
IS - 2
UR - http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a8/
LA - en
ID - IM2_1967_1_2_a8
ER -
%0 Journal Article
%A V. P. Gromov
%T On uniqueness theorems for harmonic functions in a cylinder
%J Izvestiya. Mathematics
%D 1967
%P 341-347
%V 1
%N 2
%U http://geodesic.mathdoc.fr/item/IM2_1967_1_2_a8/
%G en
%F IM2_1967_1_2_a8
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 $Q$.
[1] Evgrafov M. A., Chegis I. A., “Obobschenie teoremy Fragmena–Lindelëfa dlya analiticheskikh funktsii na garmonicheskie funktsii v prostranstve”, Dokl. AN SSSR, 134:2 (1960), 259–262 | MR | Zbl
[2] Leontev A. F., “O teoremakh tipa Fragmena–Lindelëfa dlya garmonicheskikh funktsii v tsilindre”, Izv. AN SSSR. Ser. matem., 27 (1963), 661–676 | MR