Czechoslovak Mathematical Journal, first online, pp. 1-13


Finite distortion functions and Douglas-Dirichlet functionals

Qingtian Shi

Received May 19, 2017.   Published online July 23, 2018.

Abstract:  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, $\bar{\partial}$-Dirichlet functionals of harmonic mappings are also investigated.
Keywords:  Douglas-Dirichlet functional; $\rho$-harmonic mapping; finite distortion functions; extremal quasiconformal mapping; Dirichlet's principle
Classification MSC:  30C62, 30C70, 31A05
DOI:  10.21136/CMJ.2018.0238-17

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Affiliations:   Qingtian Shi, School of Mathematics and Systems Science and Laboratory of Mathematics, Informatics and Behavioral Semantics, Beihang University, Beijing, 100191, P. R. China; School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, 362000, P. R. China. e-mail: shiqingtian2013@gmail.com


 
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