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Matematicheskie Zametki, 2007, Volume 81, Issue 3, Pages 417–426
DOI: https://doi.org/10.4213/mzm3683 (Mi mzm3683) 		 
This article is cited in 7 scientific papers (total in 7 papers)

The Mean-Value Theorem for Elliptic Operators on Stratified Sets

S. N. Oshchepkova, O. M. Penkin

Belgorod State University
Full-text PDF (502 kB) Citations (7) English version article
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DOI: https://doi.org/10.4213/mzm3683
Abstract: In this paper, an analog of the mean-value theorem for harmonic functions is proved for an elliptic operator on the stratified set of “stratified” spheres whose radius is sufficiently small. In contrast to the classical case, the statement of the theorem has the form of a special differential relationship between the mean values over different parts of the sphere. The result is used to prove the strong maximum principle.
Keywords: Green's formula, mean-value theorem, stratified sets, harmonic and subharmonic functions, strong maximum principle.
Received: 30.06.2005
English version:
Mathematical Notes, 2007, Volume 81, Issue 3, Pages 365–372
DOI: https://doi.org/10.1134/S0001434607030108
Bibliographic databases:
UDC: 517.956.4
Language: Russian
Citation: S. N. Oshchepkova, O. M. Penkin, “The Mean-Value Theorem for Elliptic Operators on Stratified Sets”, Mat. Zametki, 81:3 (2007), 417–426; Math. Notes, 81:3 (2007), 365–372
Citation in format AMSBIB
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    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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