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Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups

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Abstract

This article completes the authors’s series on stability in the Liouville theorem on the Heisenberg group. We show that every mapping with bounded distortion on a John domain of the Heisenberg group is approximated by a conformal mapping with order of closeness √K − 1 in the uniform norm and with order of closeness K − 1 in the Sobolev L 1 p -norm for all p < C/K−1. We construct two examples, demonstrating the asymptotic sharpness of our results.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    D. V. Isangulova

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  1. D. V. Isangulova
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Correspondence to D. V. Isangulova.

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Original Russian Text Copyright © 2009 Isangulova D. V.

The author was supported by the Russian Foundation for Basic Research (Grant 06-01-00735) and the State Maintenance Program for the Young Scientists and the Leading Scientific Schools of the Russian Federation (Grant NSh-5682.2008.1).

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Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 3, pp. 526–546, May–June, 2009.

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Isangulova, D.V. Stability of mappings with bounded distortion in the Sobolev norm on the John domains of Heisenberg groups. Sib Math J 50, 415–433 (2009). https://doi.org/10.1007/s11202-009-0048-x

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  • DOI: https://doi.org/10.1007/s11202-009-0048-x

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