GLOBAL HYPOELLIPTICITY, GLOBAL SOLVABILITY AND NORMAL FORM FOR A CLASS OF REAL VECTOR FIELDS ON A TORUS AND APPLICATION

被引：18
|
作者：
Petronilho, G. [1 ]
机构：
[1] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Carlos, SP, Brazil
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 363卷 / 12期
基金：
巴西圣保罗研究基金会;
关键词：
Global hypoellipticity; global solvability; normal form; OPERATORS; REGULARITY;
D O I：
10.1090/S0002-9947-2011-05359-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The main purpose of this paper is to present a class of real vector fields defined on a torus for which the concepts of global hypoellipticity and global smooth solvability are equivalent. Furthermore, such a vector field is globally hypoelliptic if and only if its adjoint is globally hypoelliptic, and therefore we can reduce it to its normal form. As an application, we study global C-infinity solvability for certain classes of sub-Laplacians.
引用
收藏
页码：6337 / 6349
页数：13
相关论文
共 50 条
  • [1] Global solvability and global hypoellipticity for a class of complex vector fields on the 3-torus
    Adalberto P. Bergamasco
    Paulo L. Dattori da Silva
    Rafael B. Gonzalez
    Alexandre Kirilov
    Journal of Pseudo-Differential Operators and Applications, 2015, 6 : 341 - 360
  • [2] Global solvability and global hypoellipticity for a class of complex vector fields on the 3-torus
    Bergamasco, Adalberto P.
    Dattori da Silva, Paulo L.
    Gonzalez, Rafael B.
    Kirilov, Alexandre
    JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2015, 6 (03) : 341 - 360
  • [3] Global solvability and global hypoellipticity in Gevrey classes for vector fields on the torus
    Bergamasco, A. P.
    Dattori da Silva, P. L.
    Gonzalez, R. B.
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (05) : 3500 - 3526
  • [4] Global solvability for a special class of vector fields on the torus
    Bergamasco, Adalberto P.
    Da Silva, Paulo L. Dattori
    Recent Progress on Some Problems in Several Complex Variables and Partial Differential Equations, 2006, 400 : 11 - 20
  • [5] Global Gevrey hypoellipticity on the torus for a class of systems of complex vector fields
    Arias Junior, Alexandre
    Kirilov, Alexandre
    de Medeira, Cleber
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 474 (01) : 712 - 732
  • [6] Global solvability and global hypoellipticity of complex vector fields on surfaces
    Hounie, Jorge
    Zugliani, Giuliano
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 340 : 616 - 641
  • [7] Global hypoellipticity and global solvability for vector fields on compact Lie groups
    Kirilov, Alexandre
    de Moraes, Wagner A. A.
    Ruzhansky, Michael
    JOURNAL OF FUNCTIONAL ANALYSIS, 2021, 280 (02)
  • [8] Global solvability for a class of complex vector fields on the two-torus
    Bergamasco, AP
    Cordaro, PD
    Petronilho, G
    COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2004, 29 (5-6) : 785 - 819
  • [9] Global solvability on the torus for certain classes of operators in the form of a sum of squares of vector fields
    Petronilho, G
    JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 145 (01) : 101 - 118
  • [10] Global hypoellipticity and global solvability for a class of operators on compact manifolds
    Bergamasco, AP
    Caetano, PAS
    Kondo, CI
    JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 141 (02) : 236 - 253
12345