Geodesic
On Poletsky-type modulus inequalities for some classes of mappings
Vladikavkazskij matematičeskij žurnal, Tome 24 (2022) no. 4, pp. 58-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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It is well-known that the theory of mappings with bounded distortion was laid by Yu. G. Reshetnyak in 60-th of the last century [1]. In papers [2, 3], there was introduced the two-index scale of mappings with weighted bounded $(q, p)$-distortion. This scale of mappings includes, in particular, mappings with bounded distortion mentioned above (under $q=p=n$ and the trivial weight function). In paper [4], for the two-index scale of mappings with weighted bounded $(q, p)$-distortion, the Poletsky-type modulus inequality was proved under minimal regularity; many examples of mappings were given to which the results of [4] can be applied. In this paper we show how to apply results of [4] to one such class. Another goal of this paper is to exhibit a new class of mappings in which Poletsky-type modulus inequalities is valid. To this end, for $n=2$, we extend the validity of the assertions in [4] to the limiting exponents of summability: $1. This generalization contains, as a special case, the results of recently published papers. As a consequence of our results, we also obtain estimates for the change in capacitу of condensers. 
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S. K. Vodopyanov. On Poletsky-type modulus inequalities for some classes of mappings. Vladikavkazskij matematičeskij žurnal, Tome 24 (2022) no. 4, pp. 58-69. http://geodesic.mathdoc.fr/item/VMJ_2022_24_4_a4/

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