On the absence of Poincaré lemma for some systems of partial differential equations

Mauro Nacinovich

Compositio Mathematica (1981)

  • Volume: 44, Issue: 1-3, page 241-303
  • ISSN: 0010-437X

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Nacinovich, Mauro. "On the absence of Poincaré lemma for some systems of partial differential equations." Compositio Mathematica 44.1-3 (1981): 241-303. <http://eudml.org/doc/89518>.

@article{Nacinovich1981,
author = {Nacinovich, Mauro},
journal = {Compositio Mathematica},
keywords = {asymptotic operators; complex of differential operators with smooth coefficients; subprincipal complexes; Poincare lemma for differential complexes},
language = {eng},
number = {1-3},
pages = {241-303},
publisher = {Sijthoff et Noordhoff International Publishers},
title = {On the absence of Poincaré lemma for some systems of partial differential equations},
url = {http://eudml.org/doc/89518},
volume = {44},
year = {1981},
}

TY - JOUR
AU - Nacinovich, Mauro
TI - On the absence of Poincaré lemma for some systems of partial differential equations
JO - Compositio Mathematica
PY - 1981
PB - Sijthoff et Noordhoff International Publishers
VL - 44
IS - 1-3
SP - 241
EP - 303
LA - eng
KW - asymptotic operators; complex of differential operators with smooth coefficients; subprincipal complexes; Poincare lemma for differential complexes
UR - http://eudml.org/doc/89518
ER -

References

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  1. [0] A. Andreotti, C.D. Hill: "E.E. Levi Convexity and the Hans Lewy Problem. Part II: Vanishing Theorems" Ann. Scuola Normale Superiore Pisa, vol. XXVI, (4) (1972), pp. 747-806. Zbl0283.32013MR477150
  2. [1] A. Andreotti, M. Nacinovich: "Some Remarks on Formal Poincaré Lemma " in "Complex Analysis and Algebraic Geometry" A collection of Papers dedicated to K. Kodaira, edited by W.L. Baily and T. Shioda. pp. 295-305Iwanami Shoten, Tokyo, 1977. Zbl0408.58028MR474424
  3. [2] A. Andreotti, M. Nacinovich: "On Analytic and C∞ Poincaré Lemma" in "Mathematical Analysis and Applications"Advances in Mathematics supplementary studies, vol. 7A, pp. 41-93. Academic Press. Chicago1981. Zbl0471.58021
  4. [3] A. Andreotti, G. Fredricks, M. Nacinovich: "On the absence of Poincaré Lemma in Tangential Cauchy-Riemann Complexes." Ann. Scuola Normale Superiore Pisa, (4) 8, 1981. Zbl0482.35061MR634855
  5. [4] J.E. Bjork: "Rings of Differential Operators." North Holland, New York, 1979. Zbl0499.13009MR549189
  6. [5] L. Boutet De Monvel: "Hypoelliptic Operators with Double Characteristics and Related Pseudo-Differential Operators." Comm. on Pure and Appl. Math., vol. XXVII, (1974) pp. 585-639. Zbl0294.35020MR370271
  7. [6] V.V. Grušin: "On a class of elliptic Pseudodifferential Operators Degenerate on a Submanifold." Math. U.S.S.R. Sbomik vol. 13 (1971) pp. 155-185. Zbl0238.47038
  8. [7] L. Hörmander: "Linear Partial Differential Operators" Springer. New York, 1963. Zbl0108.09301
  9. [8] L. Hörmander: "Pseudo-differential Operators and non-elliptic Boundary Problems." Ann. Math.83 (1966) pp. 129-209. Zbl0132.07402MR233064
  10. [9] L. Hörmander: "The Weyl Calculus of Pseudo-Differential Operators." Comm. on Pure and Appl. Math., vol. XXXII, (1979) pp. 359-443. Zbl0388.47032MR517939
  11. [10] L. Hörmander: "On the Subelliptic Test Estimates." Comm. on Pure and Appl. Math., vol. XXXIII, (1980) pp. 339-363. Zbl0414.35078MR562739
  12. [11] V. Guillemin, S. Sternberg: "Geometric Asymptotics" Math. Surveys n. 14, American Math. Society. Providence, R. I., 1977. Zbl0364.53011MR516965
  13. [12] J. Leray: "Analyse Lagrangienne et Mécanique Quantique" Séminaire sur les Equations aux Derivées Partielles. Collège de France, 1976-1977. MR501198
  14. [13] A. Melin: "Lower Bounds for Pseudo-Differential Operators " Arkiv for Matematik. vol. 9, no. 1 (1971) pp. 117-140. Zbl0211.17102MR328393
  15. [14] L. Nirenberg, F. Trèves: "On Local Solvability of Linear Partial Differential Equations. Part I : Necessary Conditions." Comm. on Pure and Appl. Math., vol. XXIII, (1970) pp. 1-38. Zbl0191.39103MR264470
  16. [15] D.G. Northcott: "Lessons on Rings, Modules and Multiplicities ". Cambridge at the University Press, 1968. Zbl0159.33001MR231816
  17. [16] J.L. Lions, E. Magenes: "Problèmes aux Limites non Homogènes et Applications. vol. 1" Paris, Dunod, 1968. Zbl0165.10801MR247243

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