N. A. Evseev, A. V. Menovschikov, “On changing variables in <nobr>$L^p$</nobr>-spaces with distributed-microstructure”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, Number 3,Pages <nobr>92

This article is cited in 2 papers

Brief communications

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

N. A. Evseev^ab, A. V. Menovschikov^ba

^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.

UDC: 517.548:517.988

Received: 08.10.2019
Revised: 08.10.2019
Accepted: 18.12.2019

DOI: 10.26907/0021-3446-2020-3-92-97