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Nonlinear Elasticity Problems on Carnot Groups and Quasiconformal Analysis. / Vodopyanov, S. K.; Pavlov, S. V.

In: Siberian Mathematical Journal, Vol. 66, No. 3, 02.06.2025, p. 672-690.

Research output: Contribution to journal › Article › peer-review

Harvard

Vodopyanov, SK & Pavlov, SV 2025, 'Nonlinear Elasticity Problems on Carnot Groups and Quasiconformal Analysis', Siberian Mathematical Journal, vol. 66, no. 3, pp. 672-690. https://doi.org/10.1134/S0037446625030085

APA

Vodopyanov, S. K., & Pavlov, S. V. (2025). Nonlinear Elasticity Problems on Carnot Groups and Quasiconformal Analysis. Siberian Mathematical Journal, 66(3), 672-690. https://doi.org/10.1134/S0037446625030085

Vancouver

Vodopyanov SK, Pavlov SV. Nonlinear Elasticity Problems on Carnot Groups and Quasiconformal Analysis. Siberian Mathematical Journal. 2025 Jun 2;66(3):672-690. doi: 10.1134/S0037446625030085

Author

Vodopyanov, S. K. ; Pavlov, S. V. / Nonlinear Elasticity Problems on Carnot Groups and Quasiconformal Analysis. In: Siberian Mathematical Journal. 2025 ; Vol. 66, No. 3. pp. 672-690.

BibTeX

@article{5bdda7ea0d064707a49cf99e400c296d,
title = "Nonlinear Elasticity Problems on Carnot Groups and Quasiconformal Analysis",
abstract = "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.",
keywords = "517.518+517.54, composition operator, distortion function, finite distortion, nonlinear elasticity, polyconvex function, quasiconformal analysis",
author = "Vodopyanov, {S. K.} and Pavlov, {S. V.}",
note = "The work of Vodopyanov was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006). The work of Pavlov was supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2025–349 dated 29.04.2025 with the Ministry of Science and Higher Education of the Russian Federation. ",
year = "2025",
month = jun,
day = "2",
doi = "10.1134/S0037446625030085",
language = "English",
volume = "66",
pages = "672--690",
journal = "Siberian Mathematical Journal",
issn = "0037-4466",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - Nonlinear Elasticity Problems on Carnot Groups and Quasiconformal Analysis

AU - Vodopyanov, S. K.

AU - Pavlov, S. V.

N1 - The work of Vodopyanov was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0006). The work of Pavlov was supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2025–349 dated 29.04.2025 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2025/6/2

Y1 - 2025/6/2

N2 - 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.

AB - 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.

KW - 517.518+517.54

KW - composition operator

KW - distortion function

KW - finite distortion

KW - nonlinear elasticity

KW - polyconvex function

KW - quasiconformal analysis

UR - https://www.mendeley.com/catalogue/28ef26af-2fd6-3e19-bef0-b9fbae43e61c/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-105007082320&origin=inward&txGid=a32bad2ebfe5fbe0726348211533ea23

U2 - 10.1134/S0037446625030085

DO - 10.1134/S0037446625030085

M3 - Article

VL - 66

SP - 672

EP - 690

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 3

ER -

ID: 67648566