This article is cited in 4 papers

Research Papers

Metaharmonic functions: mean flux theorem, its converse and related properties

N. Kuznetsov

Laboratory for Mathematical Modelling of Wave Phenomena, Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, V.O., Bol'shoy pr., 61 199178, St. Petersburg, Russia

Abstract: The mean flux theorems are proved for solutions of the Helmholtz equation and its modified version. Also, their converses are considered along with some other properties which generalise those that guarantee harmonicity.

Keywords: metaharmonic function, mean value theorem, mean flux theorem, converse theorems.

Received: 06.04.2020

Language: English

 English version: St. Petersburg Mathematical Journal, 2022, 33:2, 243–254