Abstract
The analytical theory of quasi-conformal mappings on a complex plane C implies investigating homeomorphic generalized solutions of Beltrami equation (BE) with a measurable complex-valued coefficient μ. In degenerate case, if |μ(z)|<1 for nearly all z∈C and ∥μ∥∞=ess sup |μ(z)|=1, BE may have no homeomorphic solutions, and in the case of such solution existence it can be non-unique. For degenerate BE the new existence and uniqueness theorems are established, in which, along with |μ(z)|, behavior of arg μ(z) also plays significant role.
| Original language | English |
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| Pages (from-to) | 7-9 |
| Number of pages | 3 |
| Journal | Doklady Akademii Nauk |
| Volume | 393 |
| Issue number | 1 |
| Publication status | Published - 2004 |