The main aim of this paper is to establish the Lipschitz, coLipschitz and biLipschitz continuity of quasiconformal solutions of the non-homogeneous Yukawa equations \(f_{z{\overline{z}}}(z)=(\mu (z)+\tau (z)f_z(z))f(z)\) 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.

中文翻译：

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非齐次 Yukawa 方程拟共形解的 Lipschitz 连续性

本文的主要目的是建立非齐次 Yukawa 方程的拟共形解的 Lipschitz、coLipschitz 和 biLipschitz 连续性\(f_{z{\overline{z}}}(z)=(\mu (z)+ \tau (z)f_z(z))f(z)\) 分别关于双曲度量和准双曲度量。作为应用，还讨论了在上述Yukawa方程的拟共形解下可测集的相应面积畸变。