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Mathematics. Mechanics. Informatics

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Malyutina A. N. On the continuity of some classes and subclasses of maps with an s-averaged characteristic. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2022, vol. 22, iss. 3, pp. 287-292. DOI: 10.18500/1816-9791-2022-22-3-287-292

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On the continuity of some classes and subclasses of maps with an s-averaged characteristic

Malyutina Aleksandra Nikolaevna, Tomsk State University

According to the well-known theorem of S. L. Sobolev, if $G$ is a bounded domain of Euclidean space and a function is a function having the first generalized derivatives summable with degree  $p$, then it is continuous in $G$. If $1<p\le n$  this property, generally speaking, may not be. In this paper, we find the necessary conditions under which some classes and subclasses of maps with an $s$-averaged characteristic will be continuous. Examples of subclasses of such mappings with the above properties are given in our papers.

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