# Complex vector fields and hypoelliptic partial differential operators

Andrea Altomani^{[1]}; C. Denson Hill^{[2]}; Mauro Nacinovich^{[3]}; Egmont Porten^{[4]}

- [1] University of Luxembourg Research Unity in Mathematics 162a, avenue de la Faïencerie 1511 Luxembourg (Luxembourg)
- [2] Stony Brook University Department of Mathematics Stony Brook, NY 11794 (USA)
- [3] II Università di Roma “Tor Vergata” Dipartimento di Matematica Via della Ricerca Scientifica 00133 Roma (Italy)
- [4] Sweden University Department of Mathematics 85170 Sundsvall (Sweden)

Annales de l’institut Fourier (2010)

- Volume: 60, Issue: 3, page 987-1034
- ISSN: 0373-0956

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topAltomani, Andrea, et al. "Complex vector fields and hypoelliptic partial differential operators." Annales de l’institut Fourier 60.3 (2010): 987-1034. <http://eudml.org/doc/116298>.

@article{Altomani2010,

abstract = {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 Hörmander’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.},

affiliation = {University of Luxembourg Research Unity in Mathematics 162a, avenue de la Faïencerie 1511 Luxembourg (Luxembourg); Stony Brook University Department of Mathematics Stony Brook, NY 11794 (USA); II Università di Roma “Tor Vergata” Dipartimento di Matematica Via della Ricerca Scientifica 00133 Roma (Italy); Sweden University Department of Mathematics 85170 Sundsvall (Sweden)},

author = {Altomani, Andrea, Hill, C. Denson, Nacinovich, Mauro, Porten, Egmont},

journal = {Annales de l’institut Fourier},

keywords = {Complex distribution; subelliptic estimate; hypoellipticity; Levi form; CR manifold; pseudoconcavity; flag manifold; complex distribution; subellipticity; hypoellipticity, Levi form; CR manifolds},

language = {eng},

number = {3},

pages = {987-1034},

publisher = {Association des Annales de l’institut Fourier},

title = {Complex vector fields and hypoelliptic partial differential operators},

url = {http://eudml.org/doc/116298},

volume = {60},

year = {2010},

}

TY - JOUR

AU - Altomani, Andrea

AU - Hill, C. Denson

AU - Nacinovich, Mauro

AU - Porten, Egmont

TI - Complex vector fields and hypoelliptic partial differential operators

JO - Annales de l’institut Fourier

PY - 2010

PB - Association des Annales de l’institut Fourier

VL - 60

IS - 3

SP - 987

EP - 1034

AB - 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 Hörmander’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.

LA - eng

KW - Complex distribution; subelliptic estimate; hypoellipticity; Levi form; CR manifold; pseudoconcavity; flag manifold; complex distribution; subellipticity; hypoellipticity, Levi form; CR manifolds

UR - http://eudml.org/doc/116298

ER -

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