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JOURNALS // Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya // Archive

Izv. Akad. Nauk SSSR Ser. Mat., 1968 Volume 32, Issue 4, Pages 772–779 (Mi im2490)

On the decrease of harmonic functions of three variables in a solid of revolution

I. S. Arshon


Abstract: 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.

UDC: 517.5

MSC: 47B34, 44A10, 45E05

Received: 04.01.1967


 English version:
Mathematics of the USSR-Izvestiya, 1968, 2:4, 725–733

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