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Finite distortion functions and Douglas-Dirichlet functionals

Qingtian Shi (2019)

Czechoslovak Mathematical Journal

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.

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