Solvability near the characteristic set for a class of first-order linear partial differential operators

In this work we deal with solvability of first-order differential equations in the form Lu = pu + f, where L is a planar complex vector field, elliptic everywhere except along a simple closed curve Sigma on which it is tangent and L Lambda (L) over bar vanishes of order m >= 2. In contrast with the local solvability, it is shown that the zero order term p has influence in the solvability in a full neighborhood of Sigma.