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On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals. / Водопьянов, Сергей Константинович; Павлов, Степан Валерьевич.

In: Russian Mathematics, Vol. 69, No. 6, 13.08.2025, p. 61-66.

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

Harvard

Водопьянов, СК & Павлов, СВ 2025, 'On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals', Russian Mathematics, vol. 69, no. 6, pp. 61-66. https://doi.org/10.3103/S1066369X25700483

APA

Водопьянов, С. К., & Павлов, С. В. (2025). On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals. Russian Mathematics, 69(6), 61-66. https://doi.org/10.3103/S1066369X25700483

Vancouver

Водопьянов СК, Павлов СВ. On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals. Russian Mathematics. 2025 Aug 13;69(6):61-66. doi: 10.3103/S1066369X25700483

Author

Водопьянов, Сергей Константинович ; Павлов, Степан Валерьевич. / On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals. In: Russian Mathematics. 2025 ; Vol. 69, No. 6. pp. 61-66.

BibTeX

@article{5dfea439c27e44a7946a21b7d5d36627,
title = "On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals",
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.",
author = "Водопьянов, {Сергей Константинович} and Павлов, {Степан Валерьевич}",
note = "The work is supported by the Russian Science Foundation, project no. 23-21-00359. ",
year = "2025",
month = aug,
day = "13",
doi = "10.3103/S1066369X25700483",
language = "English",
volume = "69",
pages = "61--66",
journal = "Russian Mathematics",
issn = "1066-369X",
publisher = "Allerton Press Inc.",
number = "6",

}

RIS

TY - JOUR

T1 - On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals

AU - Водопьянов, Сергей Константинович

AU - Павлов, Степан Валерьевич

N1 - The work is supported by the Russian Science Foundation, project no. 23-21-00359.

PY - 2025/8/13

Y1 - 2025/8/13

N2 - 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.

AB - 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.

U2 - 10.3103/S1066369X25700483

DO - 10.3103/S1066369X25700483

M3 - Article

VL - 69

SP - 61

EP - 66

JO - Russian Mathematics

JF - Russian Mathematics

SN - 1066-369X

IS - 6

ER -

ID: 68829026