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

We study the Gevrey solvability of a class of complex vector fields, defined on Ωϵ=(−ϵ,ϵ)×S1, given by L=∂/∂t+(a(x)+ib(x))∂/∂x, b≢0, near the characteristic set Σ={0}×S1. 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.