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.
W. Hengartner, L. Nadeau (1988)
Matematički Vesnik
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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.
Giovanni Alessandrini, Vincenzo Nesi (2002)
ESAIM: Control, Optimisation and Calculus of Variations
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This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings...
Strebel, Kurt (1998)
Annales Academiae Scientiarum Fennicae. Mathematica
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Matti Vuorinen (1983)
Banach Center Publications
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J. Achari (1978)
Matematički Vesnik
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G. Spiliopoulos (1991)
Fundamenta Mathematicae
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Rickman, Seppo (1995)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Giovanni Porru (1977)
Rendiconti del Seminario Matematico della Università di Padova
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Tadeusz Iwaniec, Gaven Martin (2002)
Studia Mathematica
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We give an example relating to the regularity properties of mappings with finite distortion. This example suggests conditions to be imposed on the distortion function in order to avoid "cavitation in measure".