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 vector fields satisfies a subelliptic estimate.
On prouve une estimation subelliptique pour les systèmes de champs vectoriels complexes sous certaines hypothèses, qui généralisent la condition de pseudoconcavité essentielle pour les variétés CR, introduite pour la première fois par deux des auteurs, et la condition de commutation d’Hörmander pour des champs vectoriels réels.
On donne des applications afin de démontrer l’hypoellipticité de systèmes de premier ordre et d’opérateurs aux dérivées partielles de second ordre.
Finalement, on décrit une classe de variétés CR compactes homogènes pour lesquelles la distribution des champs vectoriels de type satisfait une estimation subelliptique.
Keywords: Complex distribution, subelliptic estimate, hypoellipticity, Levi form, CR manifold, pseudoconcavity, flag manifold
Mot clés : distribution complexe, estimation subelliptique, hypoellipticité, forme de Levi, variété CR, pseudo-concavité
Altomani, Andrea 1; Hill, C. Denson 2; Nacinovich, Mauro 3; Porten, Egmont 4
@article{AIF_2010__60_3_987_0, author = {Altomani, Andrea and Hill, C. Denson and Nacinovich, Mauro and Porten, Egmont}, title = {Complex vector fields and hypoelliptic partial differential operators}, journal = {Annales de l'Institut Fourier}, pages = {987--1034}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {60}, number = {3}, year = {2010}, doi = {10.5802/aif.2545}, mrnumber = {2680822}, zbl = {1197.35083}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2545/} }
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 SP - 987 EP - 1034 VL - 60 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2545/ DO - 10.5802/aif.2545 LA - en ID - AIF_2010__60_3_987_0 ER -
%0 Journal Article %A Altomani, Andrea %A Hill, C. Denson %A Nacinovich, Mauro %A Porten, Egmont %T Complex vector fields and hypoelliptic partial differential operators %J Annales de l'Institut Fourier %D 2010 %P 987-1034 %V 60 %N 3 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2545/ %R 10.5802/aif.2545 %G en %F AIF_2010__60_3_987_0
Altomani, Andrea; Hill, C. Denson; Nacinovich, Mauro; Porten, Egmont. Complex vector fields and hypoelliptic partial differential operators. Annales de l'Institut Fourier, Volume 60 (2010) no. 3, pp. 987-1034. doi : 10.5802/aif.2545. https://aif.centre-mersenne.org/articles/10.5802/aif.2545/
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