TY - JOUR

T1 - Functional Properties of Limits of Sobolev Homeomorphisms with Integrable Distortion

AU - Vodopyanov, S. K.

AU - Pavlov, S. V.

PY - 2024/12/21

Y1 - 2024/12/21

N2 - The functional and geometric properties of limits of homeomorphisms with integrable distortion of domains in Carnot groups are studied. The homeomorphisms belong to Sobolev classes. Conditions are obtained under which the limits of sequences of such homeomorphisms also belong to the Sobolev class, have a finite distortion, and have the N-1-Luzin property. In the case of Carnot groups of H-type, sufficient conditions are obtained that are imposed on domains and a sequence of homeomorphisms under which the limit mapping is injective almost everywhere. These results play a key role in finding extremal solutions to problems in the mathematical theory of elasticity on H-type Carnot groups, which are the subject of subsequent works by the authors

AB - The functional and geometric properties of limits of homeomorphisms with integrable distortion of domains in Carnot groups are studied. The homeomorphisms belong to Sobolev classes. Conditions are obtained under which the limits of sequences of such homeomorphisms also belong to the Sobolev class, have a finite distortion, and have the N-1-Luzin property. In the case of Carnot groups of H-type, sufficient conditions are obtained that are imposed on domains and a sequence of homeomorphisms under which the limit mapping is injective almost everywhere. These results play a key role in finding extremal solutions to problems in the mathematical theory of elasticity on H-type Carnot groups, which are the subject of subsequent works by the authors

KW - Carnot group

KW - N-1-Luzin property

KW - class of Sobolev mappings

KW - external operator distortion function

KW - injectivity almost everywhere

KW - limit property of Sobolev mappings

KW - mapping with finite distortion

KW - Carnot group

KW - class of Sobolev mappings

KW - external operator distortion function

KW - injectivity almost everywhere

KW - limit property of Sobolev mappings

KW - mapping with finite distortion

KW - N-1-Luzin property

UR - https://www.mendeley.com/catalogue/f923199d-ce12-34dd-9aef-9b7950046dc7/

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85212880032&origin=inward&txGid=833ab14b0a6b1d588cc5007985fad5b3

U2 - 10.1007/s10958-024-07508-z

DO - 10.1007/s10958-024-07508-z

M3 - Article

VL - 286

SP - 322

EP - 342

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 3

ER -