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Sibirskii Matematicheskii Zhurnal, 2004, Volume 45, Number 4, Pages 758–779 (Mi smj1105)  
This article is cited in 1 scientific paper (total in 1 paper)

Properties of the mappings that are close to the harmonic mappings. II

A. P. Kopylov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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Abstract: We continue studying the mappings that are close to the harmonic mappings ($\varepsilon$-quasiharmonic mappings with $\varepsilon$ small). This study originates with the previous articles of the author. The results of the article include a theorem on connection between the notion of $\varepsilon$-quasiharmonic mapping and the solutions to Beltrami systems, an analog to the arithmetic mean property of harmonic functions for $\varepsilon$-quasiharmonic mappings, a theorem on stability in the Poisson formula for harmonic mappings in the ball, and a theorem on the local smoothing of $\varepsilon$-quasiharmonic mappings with $\varepsilon$ small which preserves proximity to the harmonic mappings.
Keywords: stability of classes of harmonic mappings, quasiharmonic mappings, arithmetic mean property, Poisson formula, regularization.
Received: 13.08.2001
English version:
Siberian Mathematical Journal, 2004, Volume 45, Issue 4, Pages 628–645
DOI: https://doi.org/10.1023/B:SIMJ.0000035829.53352.67
Bibliographic databases:
UDC: 517.54, 517.57, 517.95
Language: Russian
Citation: A. P. Kopylov, “Properties of the mappings that are close to the harmonic mappings. II”, Sibirsk. Mat. Zh., 45:4 (2004), 758–779; Siberian Math. J., 45:4 (2004), 628–645
Citation in format AMSBIB
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\paper Properties of the mappings that are close to the harmonic mappings.~II
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\yr 2004
\vol 45
\issue 4
\pages 758--779
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\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 4
\pages 628--645
\crossref{https://doi.org/10.1023/B:SIMJ.0000035829.53352.67}
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  • https://www.mathnet.ru/eng/smj/v45/i4/p758
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