Quasiconformal Harmonic Functions Between Convex Domains
David Kalaj (2004)
Publications de l'Institut Mathématique
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David Kalaj (2004)
Publications de l'Institut Mathématique
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David Kalaj (2011)
Studia Mathematica
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We extend the Rado-Choquet-Kneser theorem to mappings with Lipschitz boundary data and essentially positive Jacobian at the boundary without restriction on the convexity of image domain. The proof is based on a recent extension of the Rado-Choquet-Kneser theorem by Alessandrini and Nesi and it uses an approximation scheme. Some applications to families of quasiconformal harmonic mappings between Jordan domains are given.
Mateljević, M., Vuorinen, M. (2010)
Journal of Inequalities and Applications [electronic only]
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Kaljaj, David (2001)
Publications de l'Institut Mathématique. Nouvelle Série
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Kalaj, David, Pavlović, Miroslav (2005)
Annales Academiae Scientiarum Fennicae. Mathematica
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Frederick Gehring (1999)
Banach Center Publications
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Jarosław Widomski, Magdalena Gregorczyk (2010)
Annales UMCS, Mathematica
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In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition [...] . We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.
Mateljević, Miodrag (2004)
Publications de l'Institut Mathématique. Nouvelle Série
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Dariusz Partyka, Ken Sakan, Józef Zając (1999)
Banach Center Publications
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Different aspects of the boundary value problem for quasiconformal mappings and Teichmüller spaces are expressed in a unified form by the use of the trace and extension operators. Moreover, some new results on harmonic and quasiconformal extensions are included.
Miodrag Mateljević (2004)
Zbornik Radova
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Keiichi Shibata (1996)
Banach Center Publications
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Solutions to Beltrami differential equation with prescribed boundary correspondence in some plane domains are given.
Andrzej Michalski (2008)
Annales UMCS, Mathematica
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In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.
Vladimir Gutlyanskii, Olli Martio, Vladimir Ryazanov (2011)
Annales UMCS, Mathematica
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We give a quasiconformal version of the proof for the classical Lindelöf theorem: Let f map the unit disk D conformally onto the inner domain of a Jordan curve C. Then C is smooth if and only if arh f'(z) has a continuous extension to D. Our proof does not use the Poisson integral representation of harmonic functions in the unit disk.