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The paper is devoted to the study of mappings satisfying the inverse inequality of Poletsky type. Here we have studied the case when the majorant in this inequality is integrable… Click to show full abstract
The paper is devoted to the study of mappings satisfying the inverse inequality of Poletsky type. Here we have studied the case when the majorant in this inequality is integrable on some set of spheres of positive linear measure, in addition, the indicated mappings may have branch points. The local behavior of these mappings is studied, in particular, we obtained equicontinuity of their families at inner points of the domain. The most important is the result on the logarithmic Holder continuity of such mappings at inner points. As a corollary, we obtained the existence of a continuous $ACL$-solution of the Beltrami equation, which is logarithmic Holder continuous.
Journal Title: Analysis and Mathematical Physics
Year Published: 2021
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