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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.
Received: 09.07.2019 Revised: 30.10.2019 Accepted: 29.10.2019
Citation:
E. A. Shcherbakov, I. A. Avdeyev, “On the compactness of one class of quasiconformal mappings”, Probl. Anal. Issues Anal., 8(26):3 (2019), 147–151
Linking options:
https://www.mathnet.ru/eng/pa280 https://www.mathnet.ru/eng/pa/v26/i3/p147
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Abstract page: | 133 | Full-text PDF : | 45 | References: | 9 |
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