Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan

Hubert Goldschmidt

Annales scientifiques de l'École Normale Supérieure (1968)

  • Volume: 1, Issue: 3, page 417-444
  • ISSN: 0012-9593

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Goldschmidt, Hubert. "Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan." Annales scientifiques de l'École Normale Supérieure 1.3 (1968): 417-444. <http://eudml.org/doc/81837>.

@article{Goldschmidt1968,
author = {Goldschmidt, Hubert},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {partial differential equations},
language = {eng},
number = {3},
pages = {417-444},
publisher = {Elsevier},
title = {Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan},
url = {http://eudml.org/doc/81837},
volume = {1},
year = {1968},
}

TY - JOUR
AU - Goldschmidt, Hubert
TI - Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1968
PB - Elsevier
VL - 1
IS - 3
SP - 417
EP - 444
LA - eng
KW - partial differential equations
UR - http://eudml.org/doc/81837
ER -

References

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  1. [1] R. BOTT, Notes on the Spencer resolution, Mimeographed notes, Harvard University, 1963. 
  2. [2] N. BOURBAKI, Éléments de mathématique, Topologie générale ; Chapitre 2 : Structures uniformes, 4e édition, Hermann, Paris, 1965. 
  3. [3] É. CARTAN, Les systèmes différentiels extérieurs et leurs applications géométriques, Hermann, Paris, 1945. Zbl0063.00734MR7,520d
  4. [4] L. EHRENPREIS, V. W. GUILLEMIN and S. STERNBERG, On Spencer's estimate for δ-Poincaré (Ann. Math., vol. 82, 1965, p. 128-138). Zbl0178.11302MR32 #4709
  5. [5] H. GOLDSCHMIDT, Existence theorems for analytic linear partial differential equations (Ann. Math., vol. 86, 1967, p. 246-270). Zbl0154.35103MR36 #2933
  6. [6] H. GOLDSCHMIDT, Integrability criteria for systems of non linear partial differential equations (J. of Differential Geometry, vol. 1, 1967, p. 269-307). Zbl0159.14101MR37 #1746
  7. [7] A. GROTHENDIECK, Techniques de construction et théorèmes d'existence en géométrie algébrique ; IV : Les schémas de Hilbert, Séminaire Bourbaki, No. 221, 1960-1961. Zbl0236.14003
  8. [8] M. KURANISHI, On É. Cartan's prolongation theorem of exterior differential systems (Amer. J. Math., vol. 79, 1957, p. 1-47). Zbl0077.29701MR18,474d
  9. [9] M. KURANISHI, Sheaves defined by differential equations and application to deformation theory of pseudo-group structures (Amer. J. Math., vol. 86, 1964, p. 379-391). Zbl0119.07704MR29 #635
  10. [10] B. MALGRANGE, Cohomologie de Spencer (d'après QUILLEN), Séminaire mathématique, Orsay, 1966. 
  11. [11] B. MALGRANGE, Théorie analytique des équations différentielles, Séminaire Bourbaki, No. 329, 1966-1967. Zbl0186.42503
  12. [12] M. MATSUDA, Cartan-Kuranishi's prolongation of differential systems combined with that of Lagrange and Jacobi (Pub. Res. Inst. Math. Sci., Ser. A, vol. 3, 1967, p. 69-84). Zbl0172.13601MR36 #5490
  13. [13] D. MUMFORD, Lectures on curves on an algebraic surface (Ann. Math. Studies, No. 59, Princeton University Press, Princeton, 1966). Zbl0187.42701MR35 #187
  14. [14] D. G. QUILLEN, Formal properties of over-determined systems of linear partial differential equations (Ph. D. thesis, Harvard University, 1964). Zbl1295.35005
  15. [15] D. C. SPENCER, Deformation of structures on manifolds defined by transitive, continuous pseudogroups : I, II (Ann. Math., vol. 76, 1962, p. 306-445). Zbl0124.38601MR27 #6287b
  16. [16] S. STERNBERG, Notes on partial differential equations, Mimeographed notes, Harvard University (to appear). 
  17. [17] W. J. SWEENEY, The δ-Poincaré estimate (Pac. J. Math., vol. 20, 1967, p. 559-570). Zbl0152.29402MR37 #578

Citations in EuDML Documents

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  1. Hubert Goldschmidt, Prolongements d'équations différentielles linéaires. III. La suite exacte de cohomologie de Spencer
  2. Hubert Goldschmidt, Prolongations of linear partial differential equations. II. Inhomogeneous equations
  3. Katharina Neusser, Universal prolongation of linear partial differential equations on filtered manifolds
  4. Alexandre A. Martins Rodrigues, On infinite Lie groups
  5. Irene Venturi, Rigid Two-Step Nilpotent Lie Groups relative to Multicontact Structures

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