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Journal d’Analyse Mathematique

, Volume 76, Issue 1, pp 67–92 | Cite as

On solutions of the Beltrami equation

  • Melkana A. Brakalova
  • James A. Jenkins
Article

Abstract

In this paper we study the existence and uniqueness of solutions of the Beltrami equationf -z (z) =Μ(z)f z (z), whereΜ(z) is a measurable function defined almost everywhere in a plane domain ‡ with ‖ΜΜ∞ = 1-Here the partialsf z andf z of a complex valued functionf z exist almost everywhere. In case ‖Μ‖∞ ≤9 < 1, it is well-known that homeomorphic solutions of the Beltrami equation are quasiconformal mappings. In case ‖Μ‖∞= 1, much less is known. We give sufficient conditions onΜ(z) which imply the existence of a homeomorphic solution of the Beltrami equation, which isACL and whose partial derivativesf z andf z are locally inL q for anyq < 2. We also give uniqueness results. The conditions we consider improve already known results.

Keywords

Compact Subset Conformal Mapping Accumulation Point Connected Domain Quasiconformal Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 1998

Authors and Affiliations

  1. 1.Department of MathematicsThe Hotchkiss SchoolLakevilleUSA
  2. 2.Department of MathematicsWashington UniversitySt. LouisUSA

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