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ON KELLOGG'S THEOREM FOR QUASICONFORMAL MAPPINGS

  • DAVID KALAJ (a1)

Abstract

We give some extensions of classical results of Kellogg and Warschawski to a class of quasiconformal (q.c.) mappings. Among the other results we prove that a q.c. mapping f, between two planar domains with smooth C1,α boundaries, together with its inverse mapping f−1, is C1,α up to the boundary if and only if the Beltrami coefficient μf is uniformly α Hölder continuous (0 < α < 1).

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References

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1.Ahlfors, L., Lectures on quasiconformal mappings (Van Nostrand Mathematical Studies, Van Nostrand, D., 1966).
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14.Warschawski, S. E., On the higher derivatives at the boundary in conformal mapping, Trans. Amer. Math. Soc. 38 (2) (1935), 310340.
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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