Singular holomorphic solutions of linear partial differential equations with holomorphic coefficients and nonanalytic solutions of equations with analytic coefficients
Analytic solutions of partial differential equations - Trento, 1981, Astérisque, no. 89-90 (1981), pp. 223-247.
@incollection{AST_1981__89-90__223_0,
     author = {Persson, J.},
     title = {Singular holomorphic solutions of linear partial differential equations with holomorphic coefficients and nonanalytic solutions of equations with analytic coefficients},
     booktitle = {Analytic solutions of partial differential equations - Trento, 1981},
     series = {Ast\'erisque},
     pages = {223--247},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {89-90},
     year = {1981},
     mrnumber = {666411},
     zbl = {0501.35018},
     language = {en},
     url = {http://archive.numdam.org/item/AST_1981__89-90__223_0/}
}
TY  - CHAP
AU  - Persson, J.
TI  - Singular holomorphic solutions of linear partial differential equations with holomorphic coefficients and nonanalytic solutions of equations with analytic coefficients
BT  - Analytic solutions of partial differential equations - Trento, 1981
AU  - Collectif
T3  - Astérisque
PY  - 1981
SP  - 223
EP  - 247
IS  - 89-90
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_1981__89-90__223_0/
LA  - en
ID  - AST_1981__89-90__223_0
ER  - 
%0 Book Section
%A Persson, J.
%T Singular holomorphic solutions of linear partial differential equations with holomorphic coefficients and nonanalytic solutions of equations with analytic coefficients
%B Analytic solutions of partial differential equations - Trento, 1981
%A Collectif
%S Astérisque
%D 1981
%P 223-247
%N 89-90
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_1981__89-90__223_0/
%G en
%F AST_1981__89-90__223_0
Persson, J. Singular holomorphic solutions of linear partial differential equations with holomorphic coefficients and nonanalytic solutions of equations with analytic coefficients, dans Analytic solutions of partial differential equations - Trento, 1981, Astérisque, no. 89-90 (1981), pp. 223-247. http://archive.numdam.org/item/AST_1981__89-90__223_0/

[1] M. S. Baouendi, F. Treves and E. C. Zachmanoglou, Flat solutions and singular solutions of homogeneous linear partial differential equations with analytic coefficients, Duke Math. J. 46 (1979), 409-440. | DOI | MR | Zbl

[2] B. Birkeland and J. Persson, The local Cauchy problem in 2 at a point where two characteristic curves have a common tangent, J. Diff. Equations 30 (1978), 64-88. | DOI | MR | Zbl

[3] M. D. Bronšteĭn, On differential equations having non-analytic solutions, Uspehi Mat. Nauk 30 (1975), vyp. 1 (181), 227-228. | MR

[4] M. D. Bronšteĭn and V. R. Fridlender, On the characteristic Cauchy problem, Izvestija vysš. učebn. Zaved., Mat. 1978, No. 1, 188 (1978), 3-7. (In Russian). | MR | Zbl

[5] J. C. De Paris, Problème de Cauchy oscillatoire pour un opérateur différentiel à caractéristiques multiples ; lien avec 1 hyperbolicité, J. Math. Pures Appl. 51 (1972), 231-256. | MR | Zbl

[6] E. Goursat, Leçons sur l'intégration des équations aux dérivées partielles de second ordre, Tome II, Hermann, Paris, 1898. | JFM

[7] L. Hörmander, On the theory of general partial differential operators, Acta Math. 94 (1955), 161-248. | DOI | MR | Zbl

[8] L. Hörmander,Linear partial differential operators, Springer, Berlin, 1963. | MR

[9] L. Hörmander, Non-uniqueness for the Cauchy problem, in "Fourier integral operators and partial differential equations" (Coll. Int. Nice 1974), Lecture Notes in Mathematics, No. 459, Springer, Berlin/Heidelberg/New York, 1975. | DOI | MR | Zbl

[10] M. Kashiwara and P. Schapira, Problème de Cauchy pour les systèmes micro-différentiels dans le domaine complexe, Inventiones math. 46 (1978), 17-38. | DOI | EuDML | MR | Zbl

[11] H. Komatsu, Irregularity of characteristic elements and construction of nullsolutions, J. Fac. Sci. Univ. Tokyo Sect. IA 23 (1976), 297-342. | MR | Zbl

[12] H. Komatsu, Irregularity of characteristic elements and hyperbolicity, Publ. RIMS Kyoto Univ. 12, suppl. (1977), 233-245. | DOI | MR | Zbl

[13] B. Malgrange, Sur les ouverts convexes par rapport a un opérateur différentiel, C. R. Acad. Sci. Paris 254 (1962), 614-615. | MR | Zbl

[14] M. Miyake, Global and local Goursat problems in a class of holomorphic or partially holomorphic functions, J. Diff. Equations 39 (1981) 445-463. | DOI | MR | Zbl

[15] S. Mizohata, Solutions nulles et solutions non analytiques, J. Math. Kyoto Univ. 1 (1962), 271-302. | MR | Zbl

[16] J. Persson, Global and local Goursat problems for functions of Gevrey-Lednev nature. Thesis Lunds Universitet 1967. | Zbl

[17] J. Persson, New proofs and generalizations of two theorems by Lednev for Goursat problems. Math. Ann. 178 (1968), 184-208. | DOI | EuDML | MR | Zbl

[18] J. Persson, Exponential majorization and global Goursat problems, Math. Ann. 178 (1968), 271-276. | DOI | EuDML | MR | Zbl

[19] J. Persson, Non-uniqueness in the characteristic Cauchy problem when the coefficients are analytic, Matematiche 27 (1972), 145-152. | MR | Zbl

[20] J. Persson, Semi-global null solutions and P-convexity, Boll. Un. Mat. Ital. (4) 8 (1973), 20-28. | MR | Zbl

[21] J. Persson, Correction of Semi-global null solutions and P-convexity, Boll. Un. Mat. Ital. (4) 11 (1975), 518-524. | MR | Zbl

[22] J. Persson, On the Cauchy problem in n with singular data, Matematiche 30 (1975), 339-361. | MR | Zbl

[23] J. Persson, Local analytic continuation of holomorphic solutions of partial differential equations, Ann. Mat. Pura Appl. (4) 112 (1977), 193-204. | DOI | MR | Zbl

[24] J. Persson, The Cauchy problem and Hadamard's example, J. Math. Anal. Appl. 59 (1977), 522-530. | DOI | MR | Zbl

[25] J. Persson, On the analytic continuation of holomorphic solutions of partial differential equations, Preprint Università di Firenze no. 6 1979-80. | MR | Zbl

[26] J. Persson, Exponential majorization and the Cauchy problem, Séminaire Vaillant, Paris, 1979.

[27] J. Persson, Non-uniqueness of Täcklind type in the characteristic Cauchy problem, Matematiche 29 (1974), 162-175. | MR | Zbl

[28] P. Schapira, Conditions de positivité dans une varieté symplectique complexe. Application à l'étude des micro-fonctions. Submitted May 1980. | MR | Zbl

[29] S. Täcklind, Sur les classes quasianalytiques des solutions des équations aux dérivées partielles du type parabolique. Nova Acta Soc. Sci. Upsaliensis (4) 10 (1936), 1-57. | JFM

[30] A. Tihonov, Théorèmes d'unicité pour l'équation de chaleur, Mat. Sb. 42 (1935), 199-216. | EuDML | JFM

[31] F. Treves, Discrete phenomena in uniqueness in the Cauchy problem, Proc. Amer. Math. 46 (1974), 229-233. | DOI | MR | Zbl

[32] T. Yamanaka and J. Persson, On an extension of Holmgren's uniqueness theorem, Comment. Math. Univ. St. Paul. 22-1 (1973), 19-30. | MR | Zbl

[33] E. C. Zachmanoglou, Manifolds with arbitrary submanifolds of nonanalyticity of solutions of linear PDE's, Comm. Partial Differential Equations 5 (1980), 225-243. | DOI | MR | Zbl