Resumen de Global Gevrey solvability for a class of involutive systems on the torus

Adalberto P. Bergamasco, Cleber de Medeira, Sérgio Luís Zani

• Let Lj=∂/∂tj+(aj+ibj)(tj)∂/∂x, j=1,…,n, be a system of complex vector fields defined on the (n+1)-dimensional torus, where aj and bj are real-valued functions belonging to the Gevrey class Gs(T1), s>1. We present a complete characterization to the global s-solvability of this system in terms of diophantine properties of the coefficients and the Nirenberg–Treves condition (P).