On the boundary behavior of solutions of the Beltrami equations

  • D. A. Kovtonyuk Ин-т прикл. математики и механики НАН Украины, Донецк
  • I. V. Petkov Ин-т прикл. математики и механики НАН Украины, Донецк
  • V. I. Ryazanov Ин-т прикл. математики и механики НАН Украины, Донецк

Abstract

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 develop the theory of the boundary behavior and the removability of singularities of these solutions.
Published
25.08.2011
How to Cite
Kovtonyuk, D. A., I. V. Petkov, and V. I. Ryazanov. “On the Boundary Behavior of Solutions of the Beltrami Equations”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 8, Aug. 2011, pp. 1078-91, https://umj.imath.kiev.ua/index.php/umj/article/view/2786.
Section
Research articles