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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 566–584
DOI: https://doi.org/10.33048/semi.2020.17.036 (Mi semr1231) 		 
Real, complex and functional analysis

The Sobolev–Poincaré inequality and the $L_{q,p}$-cohomology of twisted cylinders

V. Gol'dsteina, Ya. A. Kopylovb

a Department of Mathematics, Ben Gurion University of the Negev, Beer Sheva, P.O.Box 653, Israel
b Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2020.17.036
Abstract: We establish a vanishing result for the $L_{q,p}$-cohomology (${q\ge p}$) of a twisted cylinder, which is a generalization of a warped cylinder. The result is new even for warped cylinders. We base on the methods for proving the $(p,q)$-Sobolev–Poincaré inequality developed by L. Shartser.
Keywords: differential form, Sobolev–Poincaré inequality, $L_{q,p}$-cohomology, twisted cylinder, homotopy operator.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0314—2019—0006
The work of the second author was carried out in the framework of the State Contract of the Sobolev Institute of Mathematics (Project 0314—2019—0006).
Received February 25, 2020, published April 16, 2020
Bibliographic databases:
Document Type: Article
UDC: 517, 515.168
MSC: 58A10, 58A12, 46E30, 55N20
Language: English
Citation: V. Gol'dstein, Ya. A. Kopylov, “The Sobolev–Poincaré inequality and the $L_{q,p}$-cohomology of twisted cylinders”, Sib. Èlektron. Mat. Izv., 17 (2020), 566–584
Citation in format AMSBIB
\Bibitem{GolKop20}
\by V.~Gol'dstein, Ya.~A.~Kopylov
\paper The~Sobolev--Poincar\'e inequality and the~$L_{q,p}$-cohomology of~twisted cylinders
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 566--584
\mathnet{http://mi.mathnet.ru/semr1231}
\crossref{https://doi.org/10.33048/semi.2020.17.036}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000529940800001}
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