On the theory of the Beltrami equation

  • V. I. Ryazanov Ин-т прикл. математики и механики НАН Украины, Донецк
  • U. Srebro
  • E. Yakubov


We study ring homeomorphisms and, on this basis, obtain a series of theorems on the existence of the so-called ring solutions for degenerate Beltrami equations. A general statement on the existence of solutions for the Beltrami equations that extends earlier results is formulated. In particular, we give new existence criteria for homeomorphic solutions $f$ of the class $W^{1, 1}_{\text{loc}}$ with f −1 ∈ $f^{—1} \in W^{1, 2}_{\text{loc}}$ in terms of tangential dilatations and functions of finite mean oscillation. The ring solutions also satisfy additional capacity inequalities.
How to Cite
Ryazanov, V. I., U. Srebro, and E. Yakubov. “On the Theory of the Beltrami Equation”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 11, Nov. 2006, pp. 1571–1583, https://umj.imath.kiev.ua/index.php/umj/article/view/3555.
Research articles