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Sur l’hypoellipticité des opérateurs pseudodifférentiels à caractéristiques multiples (perte de 3/2 derivées). (French) Zbl 0374.35012


MSC:

35H10 Hypoelliptic equations
35S99 Pseudodifferential operators and other generalizations of partial differential operators
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References:

[1] R. Beals . A General Calculus of pseudodifferential operators Duke Math . Journal Vol 42, n^\circ 1, ( 1975 ). Article | MR 51 #3972 | Zbl 0343.35078 · Zbl 0343.35078
[2] L. Boutet de Monvel . F. Trèves : On a class of pseudodifferential operators with double characteristics . Inventiones math. 24, 1. 34 ( 1974 ). MR 50 #5550 | Zbl 0281.35083 · Zbl 0281.35083
[3] L. Boutet de Monvel : Hypoelliptic operators with double characteristics and related pseudodifferential operators . Comm. pure. Appl. Math. 27, p 585-639 ( 1974 ). MR 51 #6498 | Zbl 0294.35020 · Zbl 0294.35020
[4] L. Boutet de Monvel . A. Grigis . B. Helffer (à paraître Astérisque) [5] Y.V. Egorov : Uspehi Tome 30, n^\circ 2 et 3 (182) ( 1975 ).
[5] A. Grigis : Hypoellipticité pour une classe d’opérateurs pseudo-differentiels à caractéristiques doubles et parametrixes associées (à paraître Astérisque). · Zbl 0313.35019
[6] V. V. Grusin : On a class of elliptic pseudodifferential operators degenerate on a submanifold . Mat. Sbornik Tom 84 (126) ( 1971 ) n^\circ 2, p 163-195, Math. USSR sb. 13 ( 1971 ) n^\circ 2, p 155-185. Zbl 0238.47038 · Zbl 0238.47038
[7] L. Hörmander : Pseudodifferential operators and hypoelliptic equations , Amer. Math. Soc. Symp. Pure Math., 10 ( 1966 ), p 138-183. Zbl 0167.09603 · Zbl 0167.09603
[8] L. Hörmander : A class of Hypoelliptic Pseudodifferential operators with double characteristics . Mathematishe Annalen. 217 n^\circ 2 1975 . MR 51 #13774 | Zbl 0306.35032 · Zbl 0306.35032
[9] J. Sjöstrand : Parametrices for pseudodifferential operators with multiple characteristics . Ark. för Mat. 12, p 85-130. 1974 . MR 50 #5236 | Zbl 0317.35076 · Zbl 0317.35076
[10] K. Taira : Hypoelliptic differential operators with double characteristics . Proc. Jap. Acad. 50 ( 1974 ) 124. MR 51 #13429 | Zbl 0309.35023 · Zbl 0309.35023
[11] B. Helffer : Construction de parametrixes pour des opérateurs pseudodifferentiels caractéristiques sur la réunion de deux cônes lisses . Zbl 0332.35057 · Zbl 0332.35057
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