Geodesic
Functional properties of limits of Sobolev homeomorphisms with integrable distortion
Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 2, pp. 215-236

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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 $\mathcal N^{-1}$-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.
Keywords: class of Sobolev mappings, mapping with finite distortion, external operator distortion function, limit property of Sobolev mappings, $\mathcal N^{-1}$-Luzin property, injectivity almost everywhere.
Mots-clés : Carnot group 
@article{CMFD_2024_70_2_a2,
     author = {S. K. Vodopyanov and S. Pavlov},
     title = {Functional properties of limits of {Sobolev} homeomorphisms with integrable distortion},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {215--236},
     publisher = {mathdoc},
     volume = {70},
     number = {2},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2024_70_2_a2/}
}
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S. K. Vodopyanov; S. Pavlov. Functional properties of limits of Sobolev homeomorphisms with integrable distortion. Contemporary Mathematics. Fundamental Directions, Functional spaces. Differential operators. Problems of mathematics education, Tome 70 (2024) no. 2, pp. 215-236. http://geodesic.mathdoc.fr/item/CMFD_2024_70_2_a2/