On the degenerate Beltrami equation and hydrodynamic normalization

The linear Beltrami equation on the Riemann sphere is studied under the assumption that its measurable complex-valued coefficient [micro](z) has a compact support in C and ||[micro]||[infinity] = 1. Sufficient conditions for the existence of regular homeomorphic [Please download the PDF to view the mathematical expression] solutions to the Beltrami equation with hydrodynamic normalization at infinity are given, in particular, provided that either the dilatation [Please download the PDF to view the mathematical expression] has the boundedmean-oscillation majorant or the so-called tangent dilatations [Please download the PDF to view the mathematical expression] satisfy the integral divergence conditions of the Lehto type. The corresponding applications to the degenerate A-harmonic equation associated with the Beltrami equation have also been formulated. Keywords. Bounded mean oscillation, finite mean oscillation, degenerate Beltrami equations, hydrodynamic normalization, hydromechanics, fluid mechanics.
1. Introduction The analytic theory of quasiconformal mappings f in the complex plane C is based on the Beltrami partial differential equation [Please download the PDF to view the mathematical [...]