Ring homeomorphisms and prime ends

Vladimir Gutlyanskii, Vladimir Ryazanov, Eduard Yakubov

We show that every homeomorphic $W_{\mathrm{loc}}^{1,1}$ solution $f$ of a Beltrami equation $\overline{\partial }f=\mu \partial f$ in a domain $D\subseteq \mathbb{C}$ is the so--called ring $…