On the degenerate Beltrami equation and hydrodynamic normalization

The linear Beltrami equation on the Riemann sphere is studied under assumption that its measurable complex-valued coefficient μ(z) has a compact support in ℂ and ‖μ‖∞ = 1 Sufficient conditions for existence of regular homeomorphic $$ {W}_{\mathrm{loc}}^{1,1} solutions to with hydrodynamic normalization at infinity are given, particular, provided either dilatation Kμ boundedmean- oscillation majorant or so-called tangent dilatations {K}_{\mu}^T satisfy integral divergence Lehto type. corresponding applications degenerate A-harmonic associated have also been formulated.