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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 6, Pages 1128–1152
DOI: https://doi.org/10.33048/smzh.2024.65.606 (Mi smj7914) 		 
Composition operators in Sobolev spaces on Riemannian manifolds

S. K. Vodopyanov

Sobolev Institute of Mathematics, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/smzh.2024.65.606
Abstract: Under study are the measurable mappings of Riemannian manifolds which induce bounded operators in Sobolev spaces in accordance with the change-of-variables rule. We obtain an equivalent description of the mappings and a few of their additional properties.
Keywords: Riemannian manifold, ACL-mapping, mappings of finite distortion, exterior operator distortion function, composition operator and its description, Luzin's N−1-property.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0006
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF-2022–0006).
Received: 04.08.2024
Revised: 04.08.2024
Accepted: 23.10.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 6, Pages 1305–1326
DOI: https://doi.org/10.1134/S0037446624060065
Document Type: Article
UDC: 517.518+517.54
MSC: 35R30
Language: Russian
Citation: S. K. Vodopyanov, “Composition operators in Sobolev spaces on Riemannian manifolds”, Sibirsk. Mat. Zh., 65:6 (2024), 1128–1152; Siberian Math. J., 65:6 (2024), 1305–1326
Citation in format AMSBIB
\Bibitem{Vod24}
\by S.~K.~Vodopyanov
\paper Composition operators in Sobolev~spaces on Riemannian manifolds
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 6
\pages 1128--1152
\mathnet{http://mi.mathnet.ru/smj7914}
\crossref{https://doi.org/10.33048/smzh.2024.65.606}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 6
\pages 1305--1326
\crossref{https://doi.org/10.1134/S0037446624060065}
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