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Izv. Vyssh. Uchebn. Zaved. Mat., 2020, Number 3, Pages 92–97 (Mi ivm9555)  

Brief communications

On changing variables in $L^p$-spaces with distributed-microstructure

N. A. Evseevab, A. V. Menovschikovba

a Novosibirsk State University, 1 Pirogov str., Novosibirsk, 630090 Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, 4 Ac. Koptyug Ave., Novosibirsk, 630090 Russia

Abstract: We study the boundedness of the composition operator in the spaces $L^p(V, W^{1,r}(Y_v))$. Such spaces arise when modeling the transport processes in a porous medium. It is assumed that the operator is induced by a mapping preserving the priority of the variables, which agrees with the physical requirements for the model.

Keywords: composition operator, Sobolev spaces, direct integral of Banach spaces.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-31-00089


DOI: https://doi.org/10.26907/0021-3446-2020-3-92-97

Full text: PDF file (1341 kB)
First page: PDF file
References: PDF file   HTML file

UDC: 517.548:517.988
Received: 08.10.2019
Revised: 08.10.2019
Accepted: 18.12.2019

Citation: N. A. Evseev, A. V. Menovschikov, “On changing variables in $L^p$-spaces with distributed-microstructure”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 3, 92–97

Citation in format AMSBIB
\Bibitem{EvsMen20}
\by N.~A.~Evseev, A.~V.~Menovschikov
\paper On changing variables in $L^p$-spaces with distributed-microstructure
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 3
\pages 92--97
\mathnet{http://mi.mathnet.ru/ivm9555}
\crossref{https://doi.org/10.26907/0021-3446-2020-3-92-97}


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