On regular solutions of the Dirichlet problem for the Beltrami equations

Abstract

A series of new criteria have been established for the existence of regular solutions of the Dirichlet problem for the Beltrami equations and, in particular, interims of majorants for dilatations of finite mean oscillation. Moreover, integral criteria of the type of Lehto–Miklyukov–Suvorov–Zorich are given.

Keywords:

• regular solutions
• Beltrami equation
• moduli and capacities
• paths families
• Dirichlet problem
• bounded and finite mean oscillation

AMS Subject Classifications::

• Primary 30C65
• Secondary 30C75

Acknowledgement

I would like to thank Professor Vladimir Ryazanov for his scientific supervision.