Czechoslovak Mathematical Journal, Vol. 69, No. 1, pp. 183-195, 2019
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.
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