The degree of regularity of a quasiconformal mapping

Koskela, Pekka

doi:10.1090/S0002-9939-1994-1204381-8

The degree of regularity of a quasiconformal mapping
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by Pekka Koskela

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

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

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Abstract:

T. Iwaniec has conjectured that the derivative of a locally $\alpha$-Hölder continuous quasiconformal mapping of ${\mathbb {R}^n}$ is locally integrable to any power $p < \frac {n}{{1 - \alpha }}$. We disprove this conjecture by producing examples of quasiconformal mappings of the plane that are uniformly Hölder continuous with exponent $\frac {1}{2} < \alpha < 1$ but whose derivatives are not locally integrable to the power $\frac {1}{{1 - \alpha }}$.

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