Global solvability and global hypoellipticity in Gevrey classes for vector fields on the torus

被引：14

作者：

Bergamasco, A. P. ^{[1
]}

Dattori da Silva, P. L. ^{[1
]}

Gonzalez, R. B. ^{[2
]}

机构：

[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP, Brazil

[2] Univ Fed Parana, Dept Matemat, Caixa Postal 19081, BR-81531990 Curitiba, Parana, Brazil

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2018年 / 264卷 / 05期

基金：

巴西圣保罗研究基金会;

关键词：

Gevrey solvability; Gevrey hypoellipticity; Vector fields; Periodic solutions; Fourier series;

D O I：

10.1016/j.jde.2017.11.022

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let L = partial derivative/partial derivative t + Sigma(N)(j=1) (a(j)+ib(j)) (t) partial derivative/partial derivative x(j) be a vector field defined on the torus TN+1 similar or equal to RN+1 /2 Pi Z(N+1,) where a(j),b(j) are real-valued functions and belonging to the Gevrey class G(s)(T-1), s > 1, for j= 1,..., N. We present a complete characterization for the s-global solvability and s-global hypoellipticity of L. Our results are linked to Diophantine properties of the coefficients and, also, connectedness of certain sublevel sets. (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：3500 / 3526

页数：27

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