Geodesic
On Quasilinear Beltrami-Type Equations with Degeneration
Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 445-453.

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We consider the solvability problem for the equation $f_{\overline{z}}=\nu(z,f(z)) f_z$, where the function $\nu(z,w)$ of two variables can be close to unity. Such equations are called quasilinear Beltrami-type equations with ellipticity degeneration. We prove that, under some rather general conditions on $\nu(z,w)$, the above equation has a regular homeomorphic solution in the Sobolev class $W_{\operatorname{loc}}^{1,1}$. Moreover, such solutions $f$ satisfy the inclusion $f^{\,-1}\in W_{\operatorname{loc}}^{1,2}$.
Keywords: quasilinear Beltrami-type equation, existence theorem, regular homeomorphic solution, Sobolev class, homeomorphism, Carathéodory condition, function of bounded mean oscillation. 
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E. A. Sevost'yanov. On Quasilinear Beltrami-Type Equations with Degeneration. Matematičeskie zametki, Tome 90 (2011) no. 3, pp. 445-453. http://geodesic.mathdoc.fr/item/MZM_2011_90_3_a9/

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