A1 Refereed original research article in a scientific journal
On the degenerate Beltrami equation
Authors: Gutlyanskiǐ V., Martio O., Sugawa T., Vuorinen M.
Publication year: 2005
Journal:: Transactions of the American Mathematical Society
Journal name in source: Transactions of the American Mathematical Society
Volume: 357
Issue: 3
First page : 875
Last page: 900
Number of pages: 26
ISSN: 0002-9947
DOI: https://doi.org/10.1090/S0002-9947-04-03708-0
Web address : http://api.elsevier.com/content/abstract/scopus_id:14844337558
Abstract
We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient μ(z) has the norm ∥μ∥ = 1. Sufficient conditions for the existence of a homeomorphic solution to the Beltrami equation on the Riemann sphere are given in terms of the directional dilatation coefficients of μ. A uniqueness theorem is also proved when the singular set Sing(μ) of μ is contained in a totally disconnected compact set with an additional thinness condition on Sing(μ). © 2004 American Mathematical Society.
We study the well-known Beltrami equation under the assumption that its measurable complex-valued coefficient μ(z) has the norm ∥μ∥ = 1. Sufficient conditions for the existence of a homeomorphic solution to the Beltrami equation on the Riemann sphere are given in terms of the directional dilatation coefficients of μ. A uniqueness theorem is also proved when the singular set Sing(μ) of μ is contained in a totally disconnected compact set with an additional thinness condition on Sing(μ). © 2004 American Mathematical Society.
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