Overdetermined systems of linear partial differential equations
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- by D. C. Spencer PDF
- Bull. Amer. Math. Soc. 75 (1969), 179-239
References
-
1. R. Bott, Notes on the Spencer resolution, Harvard University, Cambridge, Mass., 1963.
- C. Buttin, Existence of a homotopy operator for Spencer’s sequence in the analytic case, Pacific J. Math. 21 (1967), 219–240. MR 215324, DOI 10.2140/pjm.1967.21.219 3. H. Cartan, Familles d’espaces complexes et fondements de la géométrie analytique, Séminaire Henri Cartan, 1961/62, Secrétariat Mathématique, Paris, 1963.
- Bohumil Cenkl, Vanishing theorem for an elliptic differential operator, J. Differential Geometry 1 (1967), 381–418. MR 232410
- Leon Ehrenpreis, Victor W. Guillemin, and Shlomo Sternberg, On Spencer’s estimate for $\delta$-Poincaré, Ann. of Math. (2) 82 (1965), 128–138. MR 187256, DOI 10.2307/1970565
- Hubert Goldschmidt, Existence theorems for analytic linear partial differential equations, Ann. of Math. (2) 86 (1967), 246–270. MR 219859, DOI 10.2307/1970689
- Hubert Goldschmidt, Integrability criteria for systems of nonlinear partial differential equations, J. Differential Geometry 1 (1967), 269–307. MR 226156
- Hubert Goldschmidt, Prolongations of linear partial differential equations. I. A conjecture of Élie Cartan, Ann. Sci. École Norm. Sup. (4) 1 (1968), 417–444. MR 235584, DOI 10.24033/asens.1168
- Hubert Goldschmidt, Prolongations of linear partial differential equations. II. Inhomogeneous equations, Ann. Sci. École Norm. Sup. (4) 1 (1968), 617–625. MR 243557, DOI 10.24033/asens.1173 6. H. Goldschmidt, (e) Estimates for analytic partial differential equations (to appear).
- A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. II, Inst. Hautes Études Sci. Publ. Math. 24 (1965), 231 (French). MR 199181
- Victor Guillemin, Some algebraic results concerning the characteristics of overdetermined partial differential equations, Amer. J. Math. 90 (1968), 270–284. MR 223724, DOI 10.2307/2373436
- Victor Guillemin and Masatake Kuranishi, Some algebraic results concerning involutive subspaces, Amer. J. Math. 90 (1968), 1307–1320. MR 240839, DOI 10.2307/2373301
- V. Guillemin, D. Quillen, and S. Sternberg, The classification of the complex primitive infinite pseudogroups, Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 687–690. MR 203746, DOI 10.1073/pnas.55.4.687
- Lars Hörmander, Linear partial differential operators, Die Grundlehren der mathematischen Wissenschaften, Band 116, Springer-Verlag New York, Inc., New York, 1969. Third revised printing. MR 0248435, DOI 10.1007/978-3-662-30722-9
- Lars Hörmander, Pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 501–517. MR 180740, DOI 10.1002/cpa.3160180307
- Lars Hörmander, Pseudo-differential operators and non-elliptic boundary problems, Ann. of Math. (2) 83 (1966), 129–209. MR 233064, DOI 10.2307/1970473
- J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds. I, Ann. of Math. (2) 78 (1963), 112–148. MR 153030, DOI 10.2307/1970506
- J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds. II, Ann. of Math. (2) 79 (1964), 450–472. MR 208200, DOI 10.2307/1970404
- J. J. Kohn, Boundaries of complex manifolds, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 81–94. MR 0175149
- J. J. Kohn and L. Nirenberg, Non-coercive boundary value problems, Comm. Pure Appl. Math. 18 (1965), 443–492. MR 181815, DOI 10.1002/cpa.3160180305
- J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269–305. MR 176362, DOI 10.1002/cpa.3160180121
- Masatake Kuranishi, On E. Cartan’s prolongation theorem of exterior differential systems, Amer. J. Math. 79 (1957), 1–47. MR 81957, DOI 10.2307/2372381
- Masatake Kuranishi, Sheaves defined by differential equations and application to deformation theory of pseudo-group structures, Amer. J. Math. 86 (1964), 379–391. MR 163332, DOI 10.2307/2373171
- Hans Lewy, An example of a smooth linear partial differential equation without solution, Ann. of Math. (2) 66 (1957), 155–158. MR 88629, DOI 10.2307/1970121 16. B. MacKichan, A generalization to overdetermined systems of the notion of diagonal operators, Thesis, Stanford University, Stanford, Calif., 1968 (to appear). 17. B. Malgrange, (a) Cohomologie de Spencer (d’après Quillen), Secrétariat Mathématique d’Orsay, 1966.
- Bernard Malgrange, Théorie analytique des équations différentielles, Séminaire Bourbaki, Vol. 10, Soc. Math. France, Paris, 1995, pp. Exp. No. 329, 261–273 (French). MR 1610417
- Charles B. Morrey Jr., The analytic embedding of abstract real-analytic manifolds, Ann. of Math. (2) 68 (1958), 159–201. MR 99060, DOI 10.2307/1970048
- C. B. Morrey Jr., The $\bar \partial$-Neumann problem on strongly pseudo-convex manifolds, Outlines Joint Sympos. Partial Differential Equations (Novosibirsk, 1963), Acad. Sci. USSR Siberian Branch, Moscow, 1963, pp. 171–178. MR 0201798 19. D. G. Quillen, Formal properties of over-determined systems of linear partial differential equations, Thesis, Harvard University, Cambridge, Mass., 1964 (unpublished).
- Jean-Pierre Serre, Faisceaux algébriques cohérents, Ann. of Math. (2) 61 (1955), 197–278 (French). MR 68874, DOI 10.2307/1969915
- D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. I. Infinitesimal deformations of structure, Ann. of Math. (2) 76 (1962), 306–398. MR 156363, DOI 10.2307/1970277
- D. C. Spencer, Deformation of structures on manifolds defined by transitive, continuous pseudogroups. III. Structures defined by elliptic pseudogroups, Ann. of Math. (2) 81 (1965), 389–450. MR 179811, DOI 10.2307/1970623
- D. C. Spencer, A type of formal exterior differentiation associated with pseudogroups, Scripta Math. 26 (1963), 101–106 (1963). MR 166800 22. S. Sternberg, Partial differential equations, Lectures at the University of Pennsylvania, January-February, 1967 (polycopied).
- W. J. Sweeney, “The $\delta$-Poincaré estimate”, Pacific J. Math. 20 (1967), 559–570. MR 224979, DOI 10.2140/pjm.1967.20.559
- William J. Sweeney, The $D$-Neumann problem, Acta Math. 120 (1968), 223–277. MR 226662, DOI 10.1007/BF02394611
- W. J. Sweeney, A noncompact Dirichlet norm, Proc. Nat. Acad. Sci. U.S.A. 58 (1967), 2193–2195. MR 228003, DOI 10.1073/pnas.58.6.2193
- Ngô van Quê, Du prolongement des espaces fibrés et des structures infinitésimales, Ann. Inst. Fourier (Grenoble) 17 (1967), no. fasc. 1, 157–223 (French). MR 221416, DOI 10.5802/aif.255
Additional Information
- Journal: Bull. Amer. Math. Soc. 75 (1969), 179-239
- DOI: https://doi.org/10.1090/S0002-9904-1969-12129-4
- MathSciNet review: 0242200