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<p>It is known that the limit of a sequence of quasiconformal mappings, that is, homeomorphisms with bounded distortion whose distortion coefficients are jointly bounded, is either quasiconformal or a constant mapping.In this paper, it is shown that an analogous property holds, in the setting of Carnot groups of Heisenberg type, for a certain class of orientation-preserving homeomorphisms with finite distortion whose distortion function is integrable to a suitable power.This result is applied to&#xa0;the search for bijective solutions to variational problems analogous to nonlinear elasticity problems in irregular domains.</p>

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Nonlinear Elasticity Problems on Carnot Groups and Quasiconformal Analysis

  • 期刊论文

  • 发表日期：

    2025年5月1日

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  • S. K. Vodopyanov,
  • S. V. Pavlov

摘要

It is known that the limit of a sequence of quasiconformal mappings, that is, homeomorphisms with bounded distortion whose distortion coefficients are jointly bounded, is either quasiconformal or a constant mapping.In this paper, it is shown that an analogous property holds, in the setting of Carnot groups of Heisenberg type, for a certain class of orientation-preserving homeomorphisms with finite distortion whose distortion function is integrable to a suitable power.This result is applied to the search for bijective solutions to variational problems analogous to nonlinear elasticity problems in irregular domains.