On Poletsky-type modulus inequalities for some classes of mappings
Автор: Vodopyanov Sergey K.
Журнал: Владикавказский математический журнал @vmj-ru
Статья в выпуске: 4 т.24, 2022 года.
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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
Quasiconformal analysis, sobolev space, modulus of a family of curves, modulus estimate
Короткий адрес: https://sciup.org/143179311
IDR: 143179311 | DOI: 10.46698/w5793-5981-8894-o
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