Geodesic
On the module of continuity of mappings with an $s$-averaged characteristic
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 59 (2019), pp. 11-15 Cet article a éte moissonné depuis la source Math-Net.Ru

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We continue studying analytical properties of non-homeomorphic mappings with an $s$-averaged characteristic. O. Martio proposed the theory of $\mathcal{Q}$-homeomorphisms (2001). The concept of $\mathcal{Q}$-homeomorphisms was extended to maps with branching (2004). In this paper, we study analytical properties of non-homeomorphic mappings with an $s$-averaged characteristic and consider the question of continuity of mappings with an $s$-averaged characteristic. By the well-known Sobolev theorem, a function of class $W^1_{s,loc}(R^n)$ for is equivalent to a continuous function. This property does not hold when $s. The authors presented such example for mappings with an $s$-averaged characteristic in 2016. In this paper, we generalize the result obtained earlier to a more general class of mappings with an $s$-averaged characteristic. Relevant examples are built. The purpose of this paper is to indicate the necessary conditions under which mappings from classes and subclasses of mappings with an $s$-averaged characteristic $1 will be continuous. Here, $n$ is the dimension of the space, and $s$ is the averaging parameter. We proved a theorem in which we obtain necessary conditions for the continuity of such mappings that are with the abovementioned $s$. Earlier, such a result was obtained for functions of the class $W^1_{s,loc}(R^n)$. The theorem is an analogue of the Mori lemma.
Keywords: spatial mappings with an $s$-averaged characteristic, modulus of continuity, mapping class. 
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A. N. Malyutina; U. K. Asanbekov. On the module of continuity of mappings with an $s$-averaged characteristic. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 59 (2019), pp. 11-15. http://geodesic.mathdoc.fr/item/VTGU_2019_59_a1/

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