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

Adalberto P. Bergamasco; Cleber de Medeira; Sérgio L. Zani

doi:10.4171/rmi/1235

JournalsrmiVol. 37, No. 4pp. 1459–1488

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

Adalberto P. Bergamasco
Universidade de São Paulo, São Carlos, Brazil
Cleber de Medeira
Universidade Federal do Paraná, Curitiba, Brazil
Sérgio L. Zani
Universidade de São Paulo, São Carlos, Brazil

Download PDF

A subscription is required to access this article.

Abstract

Let $L_{j} = \partial / \partial t_{j} + (a_{j} + i b_{j}) (t_{j}) \partial / \partial x$ , $j = 1, \dots, n$ , be a system of complex vector fields defined on the $(n + 1)$ -dimensional torus, where $a_{j}$ and $b_{j}$ are real-valued functions belonging to the Gevrey class $G^{s} (T^{1})$ , $s > 1$ . 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).

Cite this article

Adalberto P. Bergamasco, Cleber de Medeira, Sérgio L. Zani, Global Gevrey solvability for a class of involutive systems on the torus. Rev. Mat. Iberoam. 37 (2021), no. 4, pp. 1459–1488

DOI 10.4171/RMI/1235