# Lipschitz continuity of quasiconformal solutions of the non-homogeneous Yukawa equations

Lipschitz continuity of quasiconformal solutions of the non-homogeneous Yukawa equations 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

# Lipschitz continuity of quasiconformal solutions of the non-homogeneous Yukawa equations

, Volume 12 (1) – Feb 1, 2022
15 pages

/lp/springer-journals/lipschitz-continuity-of-quasiconformal-solutions-of-the-non-kqiKwW0xxC
Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2021
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-021-00618-w
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Analysis and Mathematical PhysicsSpringer 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