Solvability of a class of first order differential operators on the torus
type: Item
instance of: scholarly article
title: Solvability of a class of first order differential operators on the torus
zbMATH Open document ID: 1469.35092
author: Marcelo F. de Almeida
author: Paulo L. Dattori da Silva
published in: Results in Mathematics
publication date: 2021-07-07T00:00:00Z
review text: The authors study global solvability and hypoellipticity on the $n$-torus of the equation $Pu=Lu+au+bu*=f$ where $L$ is a complex valued vector field and $u*$ is the complex conjugate of $u$. Because of the conjugation, $P$ is non-linear, and its study is new with respect to the most part of the preceding literature, see [\textit{A. P. Bergamasco} et al., J. Differ. Equations 264, No. 5, 3500--3526 (2018; Zbl 1395.35074)] for a recent survey.The authors extend the results already obtained for the equation in the 2-dimensional case by [\textit{A. P. Bergamasco} et al., J. Math. Anal. Appl. 416, No. 1, 166--180 (2014; Zbl 1302.35106)]. In particular, a complete study is given in the case when the coefficients of $P$ are constant, by including analysis of Gevrey solvability and hypoellipticity on the $n$-torus. The case of the variable coefficients is also considered. As standard for this kind of global problems, Diophantine conditions play an important role in the statements.
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35H10
zbMATH DE Number: 7369337
zbMATH Keywords: Gevrey functions
zbMATH Keywords: global solvability
zbMATH Keywords: global hypoellipticity
zbMATH Keywords: Vekua type equations
zbMATH Keywords: periodic solutions
zbMATH Keywords: Fourier series
MaRDI profile type: Publication
full work available at URL: s00025-021-01413-6
OpenAlex ID: W3157725456
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DOI: 10.1007/S00025-021-01413-6
description: scientific article; zbMATH DE number 7369337