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On the existence and uniqueness theorem for the degenerate Beltrami equation
Tekijät: Vuorinen M., Gutlyanskij V., Martio O., Sugawa T.
Julkaisuvuosi: 2004
Journal: Доклады Академии Наук / Doklady Biological Sciences
Tietokannassa oleva lehden nimi: Doklady Akademii Nauk
Vuosikerta: 393
Numero: 1
Aloitussivu: 7
Lopetussivu: 9
Sivujen määrä: 3
ISSN: 0869-5652
Verkko-osoite: http://api.elsevier.com/content/abstract/scopus_id:4644232974
Tiivistelmä
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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