Sevost’yanov, Е. А.
(2011)
On Quasilinear Beltrami-Type Equations
with Degeneration.
Mathematical Notes, 90 (9).
pp. 431-438.
ISSN 0001-4346
Abstract
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 .
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