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On Poletsky-type Modulus Inequalities for Some Classes of Mappings
Vodopyanov, S. K.
Vladikavkaz Mathematical Journal 2022. Vol. 24. Issue 4.
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 . 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 , 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  can be applied. In this paper we show how to apply results of  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  to the limiting exponents of summability: \(1 < q\leq p \leq \infty\). 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 capacitó of condensers.
Keywords: quasiconformal analysis, Sobolev space, modulus of a family of curves, modulus estimate
Language: English Download the full text
For citation: Vodopyanov, S. K. On Poletsky-type Modulus Inequalities for Some Classes of Mappings, Vladikavkaz Math. J., 2022, vol. 24, no. 4, pp. 58-69. DOI 10.46698/w5793-5981-8894-o
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