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

Journal Russian Mathematics
ISSN: 1066-369X , E-ISSN: 1934-810X
Output data Year: 2025, Volume: 69, Number: 6, Pages: 61–66 Pages count : 6 DOI: 10.3103/S1066369X25700483
Tags quasiconformal analysis, finite distortion, distortion function, composition operator, nonlinear elasticity, polyconvex function
Authors Vodop’yanov S.K. 1 , Pavlov S.V. 2
Affiliations
1 Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2 Novosibirsk State University, Novosibirsk, 630090 Russia

Funding (1)

1 Russian Science Foundation 23-21-00359

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.
Cite: Vodop’yanov S.K. , Pavlov S.V.
On Closure of the Class of Homeomorphisms with Integrable Distortion and the Minimization of Functionals
Russian Mathematics. 2025. V.69. N6. P.61–66. DOI: 10.3103/S1066369X25700483
Original: Водопьянов с.К. , Павлов С.В.
Замкнутость класса гомеоморфизмов с интегрируемым искажением и минимизация функционалов
Известия высших учебных заведений. Серия: Математика. 2025. №6. С.73-79. DOI: 10.26907/0021-3446-2025-6-73-79 РИНЦ OpenAlex
Dates:
Submitted: Feb 20, 2025
Accepted: Mar 26, 2025
Published online: Jul 29, 2025
Identifiers: No identifiers
Citing: Пока нет цитирований
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