BiLipschitz approximations of quasiconformal maps.
Bishop, Christopher J. (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Bishop, Christopher J. (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Miyachi, Hideki (2007)
Annales Academiae Scientiarum Fennicae. Mathematica
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Strebel, Kurt (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Luděk Kleprlík (2014)
Open Mathematics
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Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.
Sugawa, Toshiyuki (2002)
Annales Academiae Scientiarum Fennicae. Mathematica
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Bishop, Christopher J., Gutlyanskiĭ, Vladimir Ya., Martio, Olli, Vuorinen, Matti (2003)
International Journal of Mathematics and Mathematical Sciences
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Reich, Edgar (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Pekka Koskela (1994)
Revista Matemática Iberoamericana
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We establish an inverse Sobolev lemma for quasiconformal mappings and extend a weaker version of the Sobolev lemma for quasiconformal mappings of the unit ball of R to the full range 0 < p < n. As an application we obtain sharp integrability theorems for the derivative of a quasiconformal mapping of the unit ball of R in terms of the growth of the mapping.
Curt, Paula, Kohr, Gabriela (2008)
Journal of Inequalities and Applications [electronic only]
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Zakeri, Saeed (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Mayer, Volker (2000)
Annales Academiae Scientiarum Fennicae. Mathematica
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Reiner Kühnau (2011)
Annales UMCS, Mathematica
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We study a dual analogue of the class Σ(κ) of hydrodynamically normalized schlicht conformal mappings g(z) of the exterior of the unit circle with a [...] -quasiconformal extension, namely now those (non-schlicht) mappings g(z) for which g(z) has such a quasiconformal extension.