Abstract: 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 Poletskiy-type modulus inequality was proved under minimal regularity. In paper [4] many examples of mappings were given to which the results of [4] can be applied. In this paper we extend a result of [1] and show how to apply results of [4] to one such class. Another goal of this paper is to exzibit a new class of mappings in which Poletskiy-type modulus inequalities is valid. As a consequence of the results of this article, we obtain estimates of the change in capacity of condensers.

Cite: Vodopyanov S.K.
On Poletskiy-type modulus inequalities for some classes of mappings
Владикавказский математический журнал (Vladikavkaz Mathematical Journal). 2022. V.24. N4. P.57-68. DOI: 10.46698/w5793-5981-8894-o Scopus РИНЦ OpenAlex

Dates:

Submitted:	Sep 2, 2022
Published print:	Dec 28, 2022
Published online:	Dec 28, 2022

Identifiers:

Scopus:	2-s2.0-85145472718
Elibrary:	49994058
OpenAlex:	W4311391453

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DB	Citing
Scopus	1
OpenAlex	3
Elibrary	2

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