%A ?. ?. Sevost?yanov
%J Mathematical Notes
%T On Quasilinear Beltrami-Type Equations
with Degeneration
%X Abstract?We consider the solvability problem for the equation fz = ?(z, f(z))fz, where the
function ?(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 ?(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 .
%N 9
%K quasilinear Beltrami-type equation, Sobolev class, homeomorphic solution, homeomorphism,
Carathe? odory condition, function of bounded mean oscillation.
%P 431-438
%V 90
%D 2011
%L zu213993