On harmonic quasiconformal quasi-isometries.
Mateljević, M., Vuorinen, M. (2010)
Journal of Inequalities and Applications [electronic only]
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Mateljević, M., Vuorinen, M. (2010)
Journal of Inequalities and Applications [electronic only]
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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.
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.
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.
Ilkka Holopainen, Seppo Rickman (1992)
Revista Matemática Iberoamericana
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Miloš Arsenović, Miroslav Pavlović (2017)
Czechoslovak Mathematical Journal
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We prove two Dyakonov type theorems which relate the modulus of continuity of a function on the unit disc with the modulus of continuity of its absolute value. The methods we use are quite elementary, they cover the case of functions which are quasiregular and harmonic, briefly hqr, in the unit disc.
Kalaj, David, Pavlović, Miroslav (2005)
Annales Academiae Scientiarum Fennicae. Mathematica
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Kalaj, David, Mateljević, Miodrag (2008)
Novi Sad Journal of Mathematics
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Jürgen Jost (1982)
Manuscripta mathematica
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B. Bojarski, T. Iwaniec (1987)
Banach Center Publications
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Kaljaj, David (2001)
Publications de l'Institut Mathématique. Nouvelle Série
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Alfred Baldes (1982)
Manuscripta mathematica
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Kilpeläinen, Tero (1994)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Michael Dorff, Maria Nowak, Magdalena Wołoszkiewicz (2011)
Annales Polonici Mathematici
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We consider typically real harmonic univalent functions in the unit disk 𝔻 whose range is the complex plane slit along infinite intervals on each of the lines x ± ib, b > 0. They are obtained via the shear construction of conformal mappings of 𝔻 onto the plane without two or four half-lines symmetric with respect to the real axis.
Giovanni Alessandrini, Vincenzo Nesi (2010)
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...
David Kalaj (2004)
Publications de l'Institut Mathématique
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