A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä
On the degenerate Beltrami equation
Tekijät: Gutlyanskiǐ V., Martio O., Sugawa T., Vuorinen M.
Julkaisuvuosi: 2005
Lehti:: Transactions of the American Mathematical Society
Tietokannassa oleva lehden nimi: Transactions of the American Mathematical Society
Vuosikerta: 357
Numero: 3
Aloitussivu: 875
Lopetussivu: 900
Sivujen määrä: 26
ISSN: 0002-9947
DOI: https://doi.org/10.1090/S0002-9947-04-03708-0
Verkko-osoite: http://api.elsevier.com/content/abstract/scopus_id:14844337558
Tiivistelmä
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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