G. Citti, C-INFINITY REGULARITY OF SOLUTIONS OF THE LEVI EQUATION, Annales de l Institut Henri Poincare. Analyse non lineaire, 15(4), 1998, pp. 517-534
We will prove the C-infinity regularity of the classical solutions of
the equation Lu = q(1 + /gradu/(2))(3/2)/1 + u(t)(2) where Lu = u(xx)
+ u(yy) + 2u(y) - u(x)u(t)/1 + u(t)(2)u(xt) - 2u(x) + u(y)u(t)/1 + u(t
)(2)u(yt) + u(x)(2) + u(y)(2)/1 + u(t)(2)u(tt), q is an element of C-i
nfinity(Omega) and q(xi) not equal 0 for every tau is an element of Om
ega. This is a second order quasilinear equation, whose characteristic
form has zero determinant at every point, and for every function u. H
owever we will write it as a sum of squares of nonlinear vector fields
, and we will extablish the result by means of a suitable freezing met
hod. (C) Elsevier, Paris.