Global Gevrey solvability for a class of involutive systems on the torus
type: Item
instance of: scholarly article
title: Global Gevrey solvability for a class of involutive systems on the torus
zbMATH Open document ID: 1467.35007
author: Cleber de Medeira
author: Sérgio Luís Zani
author: Adalberto P. Bergamasco
published in: Revista Matemática Iberoamericana
publication date: 2021-07-05T00:00:00Z
review text: Summary: Let \(L_j={\partial}/{\partial t_j}+(a_j+ib_j)(t_j){\partial}/{\partial x}\), \(j=1,\ldots,n\), 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 \(G^s(\mathbb{T}^1)\), \(s > 1\). 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).
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35F05
Mathematics Subject Classification ID: 35N10
zbMATH DE Number: 7367558
zbMATH Keywords: global Gevrey solvability
zbMATH Keywords: complex vector fields
zbMATH Keywords: involutive systems
zbMATH Keywords: exponential Liouville vectors
zbMATH Keywords: periodic boundary conditions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/rmi/1235
OpenAlex ID: W3103011944
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DOI: 10.4171/RMI/1235
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description: scientific article; zbMATH DE number 7367558