Displaying similar documents to “Dirichlet's principle, distortion and related problems for harmonic mappings.”

Invertible harmonic mappings beyond the Kneser theorem and quasiconformal harmonic mappings

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.

Harmonic mappings in the exterior of the unit disk

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.

On Dyakonov type theorems for harmonic quasiregular mappings

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.

Finite distortion functions and Douglas-Dirichlet functionals

Qingtian Shi (2019)

Czechoslovak Mathematical Journal

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In this paper, we estimate the Douglas-Dirichlet functionals of harmonic mappings, namely Euclidean harmonic mapping and flat harmonic mapping, by using the extremal dilatation of finite distortion functions with given boundary value on the unit circle. In addition, ∂ ¯ -Dirichlet functionals of harmonic mappings are also investigated.

Harmonic mappings onto parallel slit domains

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.