COMPLEX VECTOR FIELDS AND HYPOELLIPTIC PARTIAL DIFFERENTIAL OPERATORS

被引：5

作者：

Altomani, Andrea ^{[1
]}

Hill, C. Denson ^{[2
]}

Nacinovich, Mauro ^{[3
]}

Porten, Egmont ^{[4
]}

机构：

[1] Univ Luxembourg, Res Unity Math, L-1511 Luxembourg, Luxembourg

[2] SUNY Stony Brook, Dept Math, Stony Brook, NY 11794 USA

[3] II Univ Roma Tor Vergata, Dipartimento Matemat, I-00133 Rome, Italy

[4] Mid Sweden Univ, Dept Math, S-85170 Sundsvall, Sweden

来源：

ANNALES DE L INSTITUT FOURIER | 2010年 / 60卷 / 03期

关键词：

Complex distribution; subelliptic estimate; hypoellipticity; Levi form; CR manifold; pseudoconcavity; flag manifold; CR MANIFOLDS; DERIVATIVES;

D O I：

10.5802/aif.2545

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a subelliptic estimate for systems of complex vector fields under some assumptions that generalize the essential pseudoconcavity for CR manifolds, that was first introduced by two of the authors; and the Hormander's bracket condition for real vector fields. Applications are given to prove the hypoellipticity of first order systems and second order partial differential operators. Finally we describe a class of compact homogeneous CR manifolds for which the distribution of (0,1) vector fields satisfies a subelliptic estimate.

引用

页码：987 / 1034

页数：48

共 50 条

[31] Optimal control for parameter estimation in partially observed hypoelliptic stochastic differential equations
Clairon, Quentin
Samson, Adeline
[J]. COMPUTATIONAL STATISTICS, 2022, 37 (05) : 2471 - 2491
[32] Phase-Space Weyl Calculus and Global Hypoellipticity of a Class of Degenerate Elliptic Partial Differential Operators
de Gosson, Maurice
[J]. NEW DEVELOPMENTS IN PSEUDO-DIFFERENTIAL OPERATORS, 2009, 189 : 1 - 14
[33] Optimal control for estimation in partially observed elliptic and hypoelliptic linear stochastic differential equations
Quentin Clairon
Adeline Samson
[J]. Statistical Inference for Stochastic Processes, 2020, 23 : 105 - 127
[34] Optimal control for estimation in partially observed elliptic and hypoelliptic linear stochastic differential equations
Clairon, Quentin
Samson, Adeline
[J]. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES, 2020, 23 (01) : 105 - 127
[35] A unified deep artificial neural network approach to partial differential equations in complex geometries
Berg, Jens
Nystrom, Kaj
[J]. NEUROCOMPUTING, 2018, 317 : 28 - 41
[36] ON THE LOCAL SOLVABILITY OF VECTOR FIELDS WITH CRITICAL POINTS
Treves, Francois
[J]. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2011, 10 (03) : 785 - 808
[37] On the Polya-Wiman properties of differential operators
Kim, Min-Hee
Kim, Young-One
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2016, 434 (02) : 1091 - 1105
[38] On differential equations involving the ψ-shifted fractional operators
Benjemaa, Mondher
Jerbi, Fatma
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2023, 46 (03) : 3371 - 3383
[39] Fractional powers of vector operators with first order boundary conditions
Colombo, Fabrizio
Gonzalez, Denis Deniz
Pinton, Stefano
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 2020, 151
[40] Orbits and global unique continuation for systems of vector fields
S. Berhanu
G. A. Mendoza
[J]. The Journal of Geometric Analysis, 1997, 7 (2) : 173 - 194

← 1 2 3 4 5 →