%0 Journal Article
%@ 0001-4346
%A Sevost’yanov, Е. А.
%D 2011
%F zu2:13993
%J Mathematical Notes
%K quasilinear Beltrami-type equation, Sobolev class, homeomorphic solution, homeomorphism,  Carathe´ odory condition, function of bounded mean oscillation.
%N 9
%P 431-438
%T On Quasilinear Beltrami-Type Equations  with Degeneration
%U http://eprints.zu.edu.ua/13993/
%V 90
%X Abstract—We consider the solvability problem for the equation fz = ν(z, f(z))fz, where the  function ν(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 ν(z,w), the above equation has a regular homeomorphic solution in the Sobolev  classW1,1  loc . Moreover, such solutions f satisfy the inclusion f −1 ∈ W1,2  loc .