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

• Autores: Adalberto P. Bergamasco, Cleber de Medeira, Sérgio Luís Zani
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 4, 2021, págs. 1459-1488
• Idioma: inglés
• DOI: 10.4171/rmi/1235
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• Resumen

  • 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).