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 \(\mu(z)\) has a compact support in \(\mathbb{C}\) and \(\Vert\mu\Vert_{\infty}=1\). Sufficient conditions for the existence of regular homeomorphic \(W_{\mathrm{loc}}^{1,1}\) solutions to the Beltrami equation with hydrodynamic normalization at infinity are given, in particular, provided that either the dilatation \(K_{\mu}\) has the bounded-mean-oscillation majorant or the so-called tangent dilatations \(K_{\mu}^{T}\) 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.