The main aim of this paper is to establish the Lipschitz, coLipschitz and biLipschitz continuity of quasiconformal solutions of the non-homogeneous Yukawa equations fzz¯(z)=(μ(z)+τ(z)fz(z))f(z)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$f_{z{\overline{z}}}(z)=(\mu (z)+\tau (z)f_z(z))f(z)$$\end{document} with respect to the hyperbolic metric and the quasihyperbolic metric, respectively. As applications, the corresponding area distortion of measurable sets under the quasiconformal solutions of the mentioned Yukawa equations is also discussed.
Analysis and Mathematical Physics – Springer Journals
Published: Feb 1, 2022
Keywords: Harmonic quasiconformal mapping; Non-homogeneous Yukawa PDE; (quasi)hyperbolically Lipschitz continuity; (quasi)hyperbolically coLipschitz continuity; (quasi)hyperbolic; area distortion; Primary: 26A16; 30F45; 30C62; 30C65; 31A05; Secondary: 30C20; 53C21
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