The Degenerate Case

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.