On local and global analytic and Gevrey hypoellipticity

Michael Christ

Journées équations aux dérivées partielles (1995)

  • Volume: 1995, page 1-7
  • ISSN: 0752-0360

How to cite


Christ, Michael. "On local and global analytic and Gevrey hypoellipticity." Journées équations aux dérivées partielles 1995 (1995): 1-7. <http://eudml.org/doc/93316>.

author = {Christ, Michael},
journal = {Journées équations aux dérivées partielles},
keywords = {Gevrey hypoellipticity; analytic hypoellipticity; nonlinear eigenvalue problems},
language = {eng},
pages = {1-7},
publisher = {Ecole polytechnique},
title = {On local and global analytic and Gevrey hypoellipticity},
url = {http://eudml.org/doc/93316},
volume = {1995},
year = {1995},

AU - Christ, Michael
TI - On local and global analytic and Gevrey hypoellipticity
JO - Journées équations aux dérivées partielles
PY - 1995
PB - Ecole polytechnique
VL - 1995
SP - 1
EP - 7
LA - eng
KW - Gevrey hypoellipticity; analytic hypoellipticity; nonlinear eigenvalue problems
UR - http://eudml.org/doc/93316
ER -


  1. [BG] M. S. Baouendi and C. Goulaouic, Nonanalytic-hypoellipticity for some degenerate elliptic operators, Bulletin AMS 78 (1972), 483-486. Zbl0276.35023MR45 #5567
  2. [C1] M. Christ, Analytic hypoellipticity, representations of nilpotent groups, and a nonlinear eigenvalue problem, Duke Math. J. 72 (1993), 595-639. Zbl0802.35025MR94k:35075
  3. [C2] M. Christ, A necessary condition for analytic hypoellipticity, Math. Research Letters 1 (1994), 241-248. Zbl0841.35026MR94m:35068
  4. [C3] M. Christ, Global analytic regularity in the presence of symmetry, Math. Research Letters 1 (1994), 599-563. Zbl0841.35027
  5. [C4] M. Christ, The Szegö projection need not preserve global analyticity, Annals of Math. (to appear). Zbl0851.32024
  6. [C5] M. Christ, Certain sums of squares of vector fields fail to be analytic hypoelliptic, Comm. Partial Differential Equations 16 (1991), 1695-1707. Zbl0762.35017MR92k:35056
  7. [C6] M. Christ, Gevrey and analytic hypoellipticity in dimension two, in preparation. 
  8. [CG] M. Christ and D. Geller, Counterexamples to analytic hypoellipticity for domains of finite type, Annals of Math. 235 (1992), 551-566. Zbl0758.35024MR93i:35034
  9. [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). Zbl0836.35036MR95j:35048
  10. [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. Zbl0303.35027MR52 #14597
  11. [FS] A. Friedman and M. Shinbrot, Nonlinear eigenvalue problems, Acta Math. 121 (1968), 77-128. Zbl0162.45704
  12. [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. Zbl0581.35009
  13. [HH] N. Hanges and A. A. Himonas, Singular solutions for sums of squares of vector fields, Comm. Partial Differential Equations 16 (1991), 1503-1511. Zbl0745.35011MR92i:35031
  14. [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. Zbl0458.35019MR84c:35026
  15. [H1] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer-Verlag, Berlin, 1983. Zbl0521.35002
  16. [H2] L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171. Zbl0156.10701MR36 #5526
  17. [Ke] M. V. Keldysh, On the completeness of the eigenfunctions of classes of non-selfadjoint linear operators, Russian Math. Surveys 26 (1971), 15-44. Zbl0235.47009
  18. [K] J. J. Kohn, Estimates for ∂b on pseudoconvex CR manifolds, Proc. Symp. Pure Math. 43 (1985), 207-217. Zbl0571.58027MR87c:32025
  19. [M1] G. Métivier, Une classe d'opérateurs non hypoélliptiques analytiques, Indiana Math. J. 29 (1980), 823-860. Zbl0455.35041MR82a:35029
  20. [M2] G. Métivier, Non-hypoellipticité analytique pour D2x + (x2 + y2)D2y, Comptes Rendus Acad. Sci. Paris 292 (1981), 401-404. Zbl0481.35033MR82b:35039
  21. [PR] Pham The Lai and D. Robert, Sur un problème aux valeurs propres non linéaire, Israel J. Math. 36 (1980), 169-186. Zbl0444.35065MR83b:35132
  22. [RS] L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), 247-320. Zbl0346.35030MR55 #9171
  23. [Ta1] D. Tartakoff, Local analytic hypoellipticity for □b on non-degenerate Cauchy-Riemann manifolds, Proc. Nat. Acad. Sci. USA 75 (1978), 3027-3028. Zbl0384.35020MR80g:58045
  24. [Ta2] D. Tartakoff, On the local real analyticity of solutions to □b and the ∂-Neumann problem, Acta Math. 145 (1980), 117-204. Zbl0456.35019MR81k:35033
  25. [Tp] J.-M. Trepreau, Sur l'hypoellipticité analytique microlocale des opérateurs de type principal, Comm. Partial Differential Equations 9 (1984), 1119-1146. Zbl0566.35027MR86m:58144
  26. [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. Zbl0384.35055MR58 #11867
  27. [Tr2] F. Treves, Analytic-hypoelliptic partial differential equations of principal type, Comm. Pure Appl Math. 24 (1971), 537-570. Zbl0222.35014MR45 #5569
  28. [Y] C.-C. Yu, Nonlinear eigenvalues and analytic-hypoellipticity, 1995 UCLA Ph. D. dissertation (to appear). 

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