On local and global analytic and Gevrey hypoellipticity
Journées équations aux dérivées partielles (1995), article no. 9, 7 p. 
@incollection{JEDP_1995____A9_0,
     author = {Michael Christ},
     title = {On local and global analytic and {Gevrey} hypoellipticity},
     booktitle = {},
     series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {9},
     pages = {1--7},
     publisher = {\'Ecole polytechnique},
     year = {1995},
     zbl = {0881.35026},
     mrnumber = {96h:35029},
     language = {en},
     url = {https://proceedings.centre-mersenne.org/item/JEDP_1995____A9_0/}
}
TY  - JOUR
AU  - Michael Christ
TI  - On local and global analytic and Gevrey hypoellipticity
JO  - Journées équations aux dérivées partielles
PY  - 1995
SP  - 1
EP  - 7
PB  - École polytechnique
UR  - https://proceedings.centre-mersenne.org/item/JEDP_1995____A9_0/
LA  - en
ID  - JEDP_1995____A9_0
ER  - 
%0 Journal Article
%A Michael Christ
%T On local and global analytic and Gevrey hypoellipticity
%J Journées équations aux dérivées partielles
%D 1995
%P 1-7
%I École polytechnique
%U https://proceedings.centre-mersenne.org/item/JEDP_1995____A9_0/
%G en
%F JEDP_1995____A9_0
Michael Christ. On local and global analytic and Gevrey hypoellipticity. Journées équations aux dérivées partielles (1995), article  no. 9, 7 p. https://proceedings.centre-mersenne.org/item/JEDP_1995____A9_0/

[BG] M. S. Baouendi and C. Goulaouic, Nonanalytic-hypoellipticity for some degenerate elliptic operators, Bulletin AMS 78 (1972), 483-486. | MR | Zbl

[C1] M. Christ, Analytic hypoellipticity, representations of nilpotent groups, and a nonlinear eigenvalue problem, Duke Math. J. 72 (1993), 595-639. | MR | Zbl

[C2] M. Christ, A necessary condition for analytic hypoellipticity, Math. Research Letters 1 (1994), 241-248. | MR | Zbl

[C3] M. Christ, Global analytic regularity in the presence of symmetry, Math. Research Letters 1 (1994), 599-563. | Zbl

[C4] M. Christ, The Szegö projection need not preserve global analyticity, Annals of Math. (to appear). | Zbl

[C5] M. Christ, Certain sums of squares of vector fields fail to be analytic hypoelliptic, Comm. Partial Differential Equations 16 (1991), 1695-1707. | MR | Zbl

[C6] M. Christ, Gevrey and analytic hypoellipticity in dimension two, in preparation.

[CG] M. Christ and D. Geller, Counterexamples to analytic hypoellipticity for domains of finite type, Annals of Math. 235 (1992), 551-566. | MR | Zbl

[CH] P. Cordaro and A. A. Himonas, Global analytic hypoellipticity of a class of degenerate elliptic operators on the torus, Mathematical Research Letters 1 (1994). | MR | Zbl

[DZ] M. Derridj and C. Zuily, Régularité analytique et Gevrey pour des classes d'opérateurs elliptiques paraboliques dégénérés du second ordre, Astérisque 2,3 (1973), 371-381. | MR | Zbl

[FS] A. Friedman and M. Shinbrot, Nonlinear eigenvalue problems, Acta Math. 121 (1968), 77-128. | Zbl

[GS] A. Grigis and J. Sjöstrand, Front d'onde analytique et sommes de carrés de champs de vecteurs, Duke Math. J. 52 (1985), 35-51. | Zbl

[HH] N. Hanges and A. A. Himonas, Singular solutions for sums of squares of vector fields, Comm. Partial Differential Equations 16 (1991), 1503-1511. | MR | Zbl

[He] B. Helffer, Conditions nécessaires d'hypoanalyticité pour des opérateurs invariants à gauche homogènes sur un groupe nilpotent gradué, J. Diff. Eq. 44 (1982), 460-481. | MR | Zbl

[H1] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer-Verlag, Berlin, 1983. | Zbl

[H2] L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171. | MR | Zbl

[Ke] M. V. Keldysh, On the completeness of the eigenfunctions of classes of non-selfadjoint linear operators, Russian Math. Surveys 26 (1971), 15-44. | Zbl

[K] J. J. Kohn, Estimates for ∂b on pseudoconvex CR manifolds, Proc. Symp. Pure Math. 43 (1985), 207-217. | MR | Zbl

[M1] G. Métivier, Une classe d'opérateurs non hypoélliptiques analytiques, Indiana Math. J. 29 (1980), 823-860. | MR | Zbl

[M2] G. Métivier, Non-hypoellipticité analytique pour D2x + (x2 + y2)D2y, Comptes Rendus Acad. Sci. Paris 292 (1981), 401-404. | MR | Zbl

[PR] Pham The Lai and D. Robert, Sur un problème aux valeurs propres non linéaire, Israel J. Math. 36 (1980), 169-186. | MR | Zbl

[RS] L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), 247-320. | MR | Zbl

[Ta1] D. Tartakoff, Local analytic hypoellipticity for □b on non-degenerate Cauchy-Riemann manifolds, Proc. Nat. Acad. Sci. USA 75 (1978), 3027-3028. | MR | Zbl

[Ta2] D. Tartakoff, On the local real analyticity of solutions to □b and the ∂-Neumann problem, Acta Math. 145 (1980), 117-204. | MR | Zbl

[Tp] J.-M. Trepreau, Sur l'hypoellipticité analytique microlocale des opérateurs de type principal, Comm. Partial Differential Equations 9 (1984), 1119-1146. | MR | Zbl

[Tr1] F. Treves, Analytic hypo-ellipticity of a class of pseudodifferential operators with double characteristics and applications to the ∂-Neumann problem, Comm. Partial Differential Equations 3 (1978), 475-642. | MR | Zbl

[Tr2] F. Treves, Analytic-hypoelliptic partial differential equations of principal type, Comm. Pure Appl Math. 24 (1971), 537-570. | MR | Zbl

[Y] C.-C. Yu, Nonlinear eigenvalues and analytic-hypoellipticity, 1995 UCLA Ph. D. dissertation (to appear).