Czechoslovak Mathematical Journal

, Volume 69, Issue 1, pp 183–195 | Cite as

Finite Distortion Functions and Douglas-Dirichlet Functionals

  • Qingtian ShiEmail author


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.


Douglas-Dirichlet functional ϱ-harmonic mapping finite distortion functions extremal quasiconformal mapping Dirichlet’s principle 

MSC 2010

30C62 30C70 31A05 


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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2018

Authors and Affiliations

  1. 1.School of Mathematics and Systems Science and Laboratory of Mathematics, Informatics and Behavioral SemanticsBeihang UniversityBeijingP.R. China
  2. 2.School of Mathematics and Computer ScienceQuanzhou Normal UniversityQuanzhouP.R. China

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