The Degenerate Case

  • Vladimir Gutlyanskii
  • Vladimir Ryazanov
  • Uri Srebro
  • Eduard Yakubov
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 26)

Abstract

Recall that in our notation, a µ-homeomorphism in a domain D,D ⊂ ℂ is an ACL homeomorphic solution of (B) in D; see Sect. 1.5. For some functions µ with |µ(z)| ≤ 1 a.e. and ||µ|| = 1, there are no µ-homeomorphisms, i.e., homeomorphic solutions of (B), as illustrated below in Sects. 4.1.1 and 4.1.2. Even when a µ-homeomorphism exists, it is not known whether it is unique and generates the set of all elementary solutions. As in the classical case, by an elementary solution, we mean an open and discrete solution.

Keywords

Derrick 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vladimir Gutlyanskii
    • 1
  • Vladimir Ryazanov
    • 2
  • Uri Srebro
    • 3
  • Eduard Yakubov
    • 4
  1. 1.Department of the Partial Differential Equations Institute of Applied Mathematics and MechanicsNational Academy of Sciences of UkraineDonetskUkraine
  2. 2.Department of the Function Theory Institute of Applied Mathematics and MechanicsNational Academy of Sciences of UkraineDonetskUkraine
  3. 3.Faculty of MathematicsTechnion-Israel Institute of TechnologyHaifaIsrael
  4. 4.Faculty of SciencesH.I.T. – Holon Institute of TechnologyHolonIsrael

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