On the boundary behavior of solutions of the Beltrami equations

• Date: 2011
• Main Authors: Kovtonyuk, D. A., Petkov, I. V., Ryazanov, V. I., Ковтонюк, Д. А., Петков, И. В., Рязанов, В. И.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2011
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2786
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We show that every homeomorphic solution of the Beltrami equation $\overline{\partial} f = \mu \partial f$ in the Sobolev class $W^{1, 1}_{\text{loc}}$ is a so-called lower $Q$-homeomorphism with $Q(z) = K_{\mu}(z)$, where $K_{\mu}$ is a dilatation quotient of this equation. On this basis, we deve...