Holder continuity of the traces of Sobolev functions to hypersurfaces in Carnot groups and the P-differentiability of Sobolev mappings Full article
| Journal |
Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2023, Volume: 64, Number: 4, Pages: 819-835 Pages count : 20 DOI: 10.1134/S0037446623040043 | ||
| Tags | Sobolev spaces, quasiconformal analysis, Carnot group | ||
| Authors |
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| Affiliations |
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Funding (1)
| 1 |
Министерство науки и высшего образования РФ Mathematical Center in Akademgorodok |
075-15-2019-1613, 075-15-2022-281 |
Abstract:
We study the behavior of Sobolev functions and mappings on the Carnot groups with the left invariant sub-Riemannian metric. We obtain some sufficient conditions for a Sobolev function to be locally H¨older continuous (in the Carnot–Carath´eodory metric) on almost every hypersurface of a given foliation. As an application of these results we show that a quasimonotone contact mapping of class W^1,_ν of Carnot groups is continuous, P-differentiable almost everywhere, and has the N-Luzin property.
Cite:
Basalaev S.G.
, Vodopyanov S.K.
Holder continuity of the traces of Sobolev functions to hypersurfaces in Carnot groups and the P-differentiability of Sobolev mappings
Siberian Mathematical Journal. 2023. V.64. N4. P.819-835. DOI: 10.1134/S0037446623040043 WOS Scopus РИНЦ OpenAlex
Holder continuity of the traces of Sobolev functions to hypersurfaces in Carnot groups and the P-differentiability of Sobolev mappings
Siberian Mathematical Journal. 2023. V.64. N4. P.819-835. DOI: 10.1134/S0037446623040043 WOS Scopus РИНЦ OpenAlex
Original:
Басалаев С.Г.
, Водопьянов С.К.
Непрерывность по Гёльдеру следов функций класса Соболева на гиперповерхностях групп Карно и P-дифференцируемость соболевских отображений
Сибирский математический журнал. 2023. Т.64. №4. С.700-719. DOI: 10.33048/smzh.2023.64.404 РИНЦ
Непрерывность по Гёльдеру следов функций класса Соболева на гиперповерхностях групп Карно и P-дифференцируемость соболевских отображений
Сибирский математический журнал. 2023. Т.64. №4. С.700-719. DOI: 10.33048/smzh.2023.64.404 РИНЦ
Dates:
| Submitted: | Apr 14, 2023 |
| Accepted: | May 16, 2023 |
| Published print: | Jul 21, 2023 |
| Published online: | Jul 21, 2023 |
Identifiers:
| Web of science: | WOS:001035552800004 |
| Scopus: | 2-s2.0-85165598996 |
| Elibrary: | 62232956 |
| OpenAlex: | W4385191934 |