On the existence and uniqueness theorem for the degenerate Beltrami equation

M. Vuorinen, V. Y. Gutlyanskij, O. Martio, Toshiyuki Sugawa

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)7-9
Number of pages3
JournalDoklady Akademii Nauk
Volume393
Issue number1
Publication statusPublished - 2004 Oct 5
Externally publishedYes

ASJC Scopus subject areas

  • General

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