On the compactness of one class of quasiconformal mappings

E. A. Shcherbakov, I. A. Avdeyev

Kuban State University, 149 Stavropolskaya str., Krasnodar 350040, Russia

Abstract: We consider an elliptic system in the disk ${|z|<1}$ for the so-called $p$-analytic functions. This system admits degeneration at the boundary of the disk. We prove compactness of the family of $K$-quasiconformal mappings, which are the solutions of the uniformly elliptic systems approximating the degenerating one.

Keywords: quasi-conformal mappings, sobolev spaces, elliptic systems, embedding theorems, topological mappings, Dirichlet integral, Douglas integral, harmonic functions.

UDC: 517.3

MSC: 30C70, 30C75

Received: 09.07.2019
Revised: 30.10.2019
Accepted: 29.10.2019

Language: English

DOI: 10.15393/j3.art.2019.6670

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