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Local analytic continuation of holomorphic solutions of partial differential equations. (English) Zbl 0345.35002


MSC:

35A20 Analyticity in context of PDEs
35A30 Geometric theory, characteristics, transformations in context of PDEs
32D20 Removable singularities in several complex variables
35F05 Linear first-order PDEs
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[1] Bengel, G., Sur le prolongement analytique des solutions d’une équation aux dérivées partielles, C. R. Acad. Sci. Paris Sér. A-B, 273, 572-574 (1971) · Zbl 0217.41001
[2] Bony, J.-M.; Schapira, P., Existence et prolongement de solutions holomorphes des équations aux dérivées partielles, Invent. Math., 17, 95-105 (1972) · Zbl 0225.35008
[3] John, F., On linear partial differential equations with analytic coefficients. Unique continuation of data, Comm. Pure Appl. Math., 2, 209-253 (1949) · Zbl 0035.34601
[4] Hörmander, L., Linear partial differential operators (1963), Berlin: Springer, Berlin · Zbl 0171.06802
[5] Hörmander, L., Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients, Comm. Pure Appl. Math., 24, 671-704 (1971) · Zbl 0226.35019
[6] Hörmander, L., On the existence and regularity of solutions of linear pseudo-differential equations, Enseignement Math., 17, 99-153 (1971) · Zbl 0224.35084
[7] Kiselman, C. O., Prolongement des solutions d’une équations aux dérivées partielles à coefficients constants, Bull. Soc. Math. France, 97, 329-356 (1969) · Zbl 0189.40502
[8] Leray, J., Uniformisations de la solution du problème linéaire analytique de Cauchy près de la varité qui porte les donnés de Cauchy (Problème de Cauchy I), Bull. Soc. Math. France, 85, 389-429 (1957) · Zbl 0108.09501
[9] Persson, J., On uniqueness cones, velocity cones, and P-convexity, Ann. Mat. Pura Appl., 96, 4, 69-87 (1973) · Zbl 0273.35020
[10] Persson, J., Non-uniqueness in the characteristic Cauchy problem when the coefficients are analytic, Matematiche, 27, 145-152 (1972) · Zbl 0257.35016
[11] Persson, J., Semi-global null solutions and P-convexity, Boll. Un. Mat. Ital., 8, 4, 20-28 (1973) · Zbl 0269.35013
[12] Persson, J., Correction of «Semiglobal null solutions and P-convexity», Boll. Un. Mat. Ital., 11, 4, 518-524 (1975) · Zbl 0316.35017
[13] Persson, J., New proofs and generalizations of two theorems by Lednev for Goursat problems, Math. Ann., 178, 184-208 (1968) · Zbl 0159.14701
[14] Persson, J., Non-uniqueness and uniqueness in the Cauchy problem at simple characteristic points, Math. Ann., 203, 231-238 (1973) · Zbl 0243.35082
[15] Pucci, C., Nuove ricerche sul problema di Cauchy, Mem. Acc. Sci. Torino, 1, 45-67 (1954)
[16] Tsuno, Y., On the prolungation of local holomorphic solutions of partial differential equations, J. Math. Soc. Japan, 26, 523-548 (1974) · Zbl 0279.35012
[17] Wagschal, C., Sur le problème de Cauchy ramifié, J. Math. Pures Appl., 53, 147-164 (1974) · Zbl 0265.35016
[18] Yamanaka, T.; Persson, J., On an extension of Holmgren’s uniqueness theorem, Comment. Math. Univ. St. Paul., 22, 19-30 (1973) · Zbl 0276.35020
[19] Zachmanoglou, E., Propagation of zeros and uniqueness in the Cauchy problem for first order partial differential equations, Arch. Rational Mech. Anal., 38, 178-188 (1970) · Zbl 0199.15903
[20] Zachmanoglou, E., Solutions of partial differential equations with support on leaves of associated foliations, Trans. Am. Math. Soc., 180, 415-421 (1973) · Zbl 0237.35019
[21] Zerner, M., Domaine d’holomorphie des fonctions vérifiant une équation aux dérivées partielles, C. R. Acad. Sci. Paris Sér. A-B, 272, 1646-1648 (1971) · Zbl 0213.37004
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