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D’Agnolo, Andrea; Schapira, Pierre

An inverse image theorem for sheaves with applications to the Cauchy problem. (English) Zbl 0760.35003

Duke Math. J. 64, No. 3, 451-472 (1991).
The Cauchy problem is considered by the method of sheaf theory. As an application known results are obtained related to the hyperbolic Cauchy problem in the framework of hyperfunctions.
Reviewer: V.Nazarov (Minsk)

Cited in 2 Reviews
Cited in 3 Documents

MSC:

35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
58J15 Relations of PDEs on manifolds with hyperfunctions
58C15 Implicit function theorems; global Newton methods on manifolds
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials

Citations:

Zbl 0739.58006
Cite Review PDF
Full Text: DOI

References:

[1] A. D’Agnolo, Inverse image for the functor \(\mu\,\mathrm hom\) , Publ. Res. Inst. Math. Sci. 27 (1991), no. 3, 509-532. · Zbl 0751.58041 · doi:10.2977/prims/1195169667
[2] A. D’Agnolo and P. Schapira, Un théorème d’image inverse pour les faisceaux. Applications au problème de Cauchy , C. R. Acad. Sci. Paris Sér. I Math. 311 (1990), no. 1, 23-26. · Zbl 0739.58006
[3] P. Deligne, Le formalisme des cycles évanescents , Séminaire de Géométrie Algébrique du Bois-Marie 1967-1969 (SGA 7 II), Lecture Notes in Math., vol. 340, Springer, New York, 1973, pp. 82-115. · Zbl 0266.14008
[4] A. Grothendieck, Résumé des premiers exposés de A. Grothendieck , Séminaire de Géométrie Algébrique du Bois-Marie 1967-1969 (SGA 7 I), Lecture Notes in Math., vol. 288, Springer, New York, 1972, pp. 1-24. · Zbl 0267.14003
[5] Y. Hamada, The singularities of the solutions of the Cauchy problem , Publ. Res. Inst. Math. Sci. 5 (1969), 21-40. · Zbl 0203.40702 · doi:10.2977/prims/1195194750
[6] Y. Hamada, J. Leray, and C. Wagschal, Systèmes d’équations aux dérivées partielles à caractéristiques multiples: problème de Cauchy ramifié; hyperbolicité partielle , J. Math. Pures Appl. (9) 55 (1976), no. 3, 297-352. · Zbl 0307.35056
[7] M. Kashiwara, Algebraic study of systems of partial differential equations , thesis, Tokyo, 1971, (in Japanese).
[8] M. Kashiwara, Systems of microdifferential equations , Progress in Mathematics, vol. 34, Birkhäuser Boston Inc., Boston, MA, 1983. · Zbl 0521.58057
[9] M. Kashiwara and P. Schapira, Problème de Cauchy pour les systèmes microdifférentiels dans le domaine complexe , Invent. Math. 46 (1978), no. 1, 17-38. · Zbl 0369.35061 · doi:10.1007/BF01390101
[10] M. Kashiwara and P. Schapira, Micro-hyperbolic systems , Acta Math. 142 (1979), no. 1-2, 1-55. · Zbl 0413.35049 · doi:10.1007/BF02395056
[11] M. Kashiwara and P. Schapira, Microlocal study of sheaves , Astérisque (1985), no. 128, 235. · Zbl 0589.32019
[12] M. Kashiwara and P. Schapira, Sheaves on manifolds , Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 292, Springer-Verlag, Berlin, 1990. · Zbl 0709.18001
[13] Y. Laurent, Théorie de la deuxième microlocalisation dans le domaine complexe , Progress in Mathematics, vol. 53, Birkhäuser Boston Inc., Boston, MA, 1985. · Zbl 0561.32013
[14] E. Leichtnam, Le problème de Cauchy ramifié , Ann. Sci. École Norm. Sup. (4) 23 (1990), no. 3, 369-443. · Zbl 0717.35018
[15] J. Leray, Problème de Cauchy. I. Uniformisation de la solution du problème linéaire analytique de Cauchy près de la variété qui porte les données de Cauchy , Bull. Soc. Math. France 85 (1957), 389-429. · Zbl 0108.09501
[16] T. Monteiro Fernandes, Problème de Cauchy microdifférentiel et théorèmes de propagation , C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 18, A833-A836. · Zbl 0445.58027
[17] V. E. Nazaikinskii, V. E. Shatalov, and Yu. B. Sternin, Analytic singularities of solutions of differential equations , \(D\)-modules and Microlocal Geometry, de Gruyter, New York, to appear, 1991.
[18] P. Schapira, Microdifferential systems in the complex domain , Grundlehren der Math. Wiss. [Fundamental Principles of Mathematical Sciences], vol. 269, Springer-Verlag, Berlin, 1985. · Zbl 0554.32022
[19] 1 D. Schiltz, Un domaine d’holomorphie de la solution d’un problème de Cauchy homogène , Ann. Fac. Sci. Toulouse Math. (5) 9 (1988), no. 3, 269-294. · Zbl 0694.35019 · doi:10.5802/afst.661
[20] 2 D. Schiltz, Décomposition de la solution d’un problème de Cauchy homogène près de la frontière d’un domaine d’holomorphie des données de Cauchy , C. R. Acad. Sci. Paris Sér. I Math. 306 (1988), no. 4, 177-180. · Zbl 0646.32009
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