The degree of regularity of a quasiconformal mapping

Author:
Pekka Koskela

Journal:
Proc. Amer. Math. Soc. **122** (1994), 769-772

MSC:
Primary 30C65; Secondary 30C62

DOI:
https://doi.org/10.1090/S0002-9939-1994-1204381-8

MathSciNet review:
1204381

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Abstract | References | Similar Articles | Additional Information

Abstract: T. Iwaniec has conjectured that the derivative of a locally -Hölder continuous quasiconformal mapping of is locally integrable to any power . We disprove this conjecture by producing examples of quasiconformal mappings of the plane that are uniformly Hölder continuous with exponent but whose derivatives are not locally integrable to the power .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1994-1204381-8

Keywords:
Quasiconformal mapping,
Sobolev embedding,
global integrability of the derivative

Article copyright:
© Copyright 1994
American Mathematical Society