Geodesic
On changing variables in $L^p$-spaces with distributed-microstructure
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2020), pp. 92-97

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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, direct integral of Banach spaces.
Mots-clés : Sobolev spaces 
@article{IVM_2020_3_a8,
     author = {N. A. Evseev and A. V. Menovschikov},
     title = {On changing variables in $L^p$-spaces with distributed-microstructure},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {92--97},
     publisher = {mathdoc},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_3_a8/}
}
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N. A. Evseev; A. V. Menovschikov. On changing variables in $L^p$-spaces with distributed-microstructure. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2020), pp. 92-97. http://geodesic.mathdoc.fr/item/IVM_2020_3_a8/