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Abstract <p>It is known that the limit of a sequence of (quasi)conformal mappings is either a constant or a (quasi)conformal mapping. In this paper, we prove that in the case of Heisenberg-type Carnot groups, a similar property is valid for mappings that are quasiconformal in the mean, that is, for homeomorphisms with finite distortion and a distortion function integrable to an appropriate degree. This result is applied to solving model problems of nonlinear elasticity theory on Carnot groups.</p>

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On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • S. K. Vodop’yanov,
  • S. V. Pavlov

摘要

Abstract

It is known that the limit of a sequence of (quasi)conformal mappings is either a constant or a (quasi)conformal mapping. In this paper, we prove that in the case of Heisenberg-type Carnot groups, a similar property is valid for mappings that are quasiconformal in the mean, that is, for homeomorphisms with finite distortion and a distortion function integrable to an appropriate degree. This result is applied to solving model problems of nonlinear elasticity theory on Carnot groups.