Geodesic
Finite distortion functions and Douglas-Dirichlet functionals
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 183-195

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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.
DOI : 10.21136/CMJ.2018.0238-17
Classification : 30C62, 30C70, 31A05
Keywords: Douglas-Dirichlet functional; $\rho $-harmonic mapping; finite distortion functions; extremal quasiconformal mapping; Dirichlet's principle 
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     title = {Finite distortion functions and {Douglas-Dirichlet} functionals},
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Shi, Qingtian. Finite distortion functions and Douglas-Dirichlet functionals. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 1, pp. 183-195. doi: 10.21136/CMJ.2018.0238-17

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