On the decrease of harmonic functions of three variables in a~solid of revolution
Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 725-733.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we prove a theorem on the decrease of harmonic functions of three variables in a solid of revolution $$ x>a, \quad \sqrt{{x_1}^2+{x_2}^2}\frac12h(x), $$ that is analogous to the theorem on the decrease of analytic functions in a domain.
@article{IM2_1968_2_4_a3,
     author = {I. S. Arshon},
     title = {On the decrease of harmonic functions of three variables in a~solid of revolution},
     journal = {Izvestiya. Mathematics },
     pages = {725--733},
     publisher = {mathdoc},
     volume = {2},
     number = {4},
     year = {1968},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a3/}
}
TY  - JOUR
AU  - I. S. Arshon
TI  - On the decrease of harmonic functions of three variables in a~solid of revolution
JO  - Izvestiya. Mathematics 
PY  - 1968
SP  - 725
EP  - 733
VL  - 2
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a3/
LA  - en
ID  - IM2_1968_2_4_a3
ER  - 
%0 Journal Article
%A I. S. Arshon
%T On the decrease of harmonic functions of three variables in a~solid of revolution
%J Izvestiya. Mathematics 
%D 1968
%P 725-733
%V 2
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a3/
%G en
%F IM2_1968_2_4_a3
I. S. Arshon. On the decrease of harmonic functions of three variables in a~solid of revolution. Izvestiya. Mathematics , Tome 2 (1968) no. 4, pp. 725-733. http://geodesic.mathdoc.fr/item/IM2_1968_2_4_a3/

[1] Arshon I. S., Iglitskii M. A., “Ob ubyvanii garmonicheskikh funktsii v tsilindre”, Dokl. AN SSSR, 152:4 (1963), 775–778 | Zbl

[2] Arshon I. S., Pak M. A, “Teorema edinstvennosti dlya garmonicheskikh funktsii v poluprostranstve”, Matem. sb., 68 (1965), 148–151 | MR | Zbl

[3] Arshon I. S., “Ob ubyvanii garmonicheskikh funktsii trekh peremennykh”, Izv. AN SSSR. Ser. matem., 29 (1965), 1283–1294

[4] Landis E. M., “Nekotorye voprosy kachestvennoi teorii ellipticheskikh uravnenii vtorogo poryadka (sluchai mnogikh nezavisimykh peremennykh)”, Uspekhi matem. nauk, 18:1(109) (1963), 3–62 | MR | Zbl