Abstract
We consider the solvability problem for the equation \(f_{\bar z} \) = v(z, f(z))fz, where the function v(z,w) of two variables may be close to unity. Such equations are called quasilinear Beltrami-type equations with ellipticity degeneration. We prove that, under some rather general conditions on v(z,w), the above equation has a regular homeomorphic solution in the Sobolev classWloc1,1. Moreover, such solutions f satisfy the inclusion f−1 ∈ Wloc1,2.
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