Gevrey solvability near the characteristic set for a class of planar complex vector fields of infinite type

Abstract

We study the Gevrey solvability of a class of complex vector fields, defined on Ω ϵ = ( − ϵ , ϵ ) × S 1 , given by L = ∂ / ∂ t + ( a ( x ) + i b ( x ) ) ∂ / ∂ x , b ≢ 0 , near the characteristic set Σ = { 0 } × S 1 . We show that the interplay between the order of vanishing of the functions a and b at x = 0 plays a role in the Gevrey solvability.