Sevost’yanov, Е. А.
(2011)
On Quasilinear BeltramiType Equations
with Degeneration.
Mathematical Notes, 90 (9).
pp. 431438.
ISSN 00014346
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
Beltramitype 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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