Properties of the mappings that are close to the harmonic mappings

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1998 English Publisher:Springer Science and Business Media LLCJournal:Siberian Mathematical Journal, volume 39, pages 765-780 (issn: 0037-4466, eissn: 1573-9260,

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Authors: Kopylov, A. P.;

doi: 10.1007/bf02673058 , 10.1023/b:simj.0000035829.53352.67

Properties of the mappings that are close to the harmonic mappings

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Abstract

This a continuation of the author's paper [Sib. Math. J. 39, No. 4, 765-780 (1998; Zbl 0915.30019)]. The results of the article include a theorem on the 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.

Related Organizations

Sobolev Institute of Mathematics
Russian Federation

Keywords

stability of classes of harmonic mappings, regularization, Poisson formula, Quasiconformal mappings in \(\mathbb{R}^n\), other generalizations, arithmetic mean property, quasiharmonic mappings, Other generalizations (nonlinear potential theory, etc.)

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