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Keywords:
Douglas-Dirichlet functional; $\rho $-harmonic mapping; finite distortion functions; extremal quasiconformal mapping; Dirichlet's principle
Douglas-Dirichlet functional; $\rho $-harmonic mapping; finite distortion functions; extremal quasiconformal mapping; Dirichlet's principle
Summary:
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.
References:
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