A1 Refereed original research article in a scientific journal
On the existence and uniqueness theorem for the degenerate Beltrami equation
Authors: Vuorinen M., Gutlyanskij V., Martio O., Sugawa T.
Publication year: 2004
Journal: Доклады Академии Наук / Doklady Biological Sciences
Journal name in source: Doklady Akademii Nauk
Volume: 393
Issue: 1
First page : 7
Last page: 9
Number of pages: 3
ISSN: 0869-5652
Web address : http://api.elsevier.com/content/abstract/scopus_id:4644232974
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.
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.
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