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Book Review
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Book Information
Author(s):
Sigeru Mizohata
Title:
On the Cauchy problem
Additional book information:
Science Press, Beijing, and Academic Press, Orlando, 1985, 177 pp., $36.00 (paper). ISBN 0-12-501660-3
References:
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- 2.
- A. P. Calderón and A. Zygmund, On the existence of certain singular integrals, Acta Math. 88 (1952), 85-139. MR 52553
- 3.
- A. P. Calderón and A. Zygmund, Singular integral operators and differential equations, Amer. J. Math. 79 (1957), 901-921. MR 100768
- 4.
- A. Cauchy, Mémoire sur un théorème fondamental dans le calcul intégral, C. R. Acad. Sci. Paris 14 (1842), 1020.
- 5.
- A. Cauchy, Mémoire sur l'emploi du calcul des limites dans l'integration des équations aux dérivées partielles, C. R. Acad. Sci. Paris 15 (1842), 44.
- 6.
- A. Cauchy, Mémoire sur l'application du calcul des limites à rintegration d'un système d 'equations aux dérivées partielles, C. R. Acad. Sci. Paris 15 (1842), 85.
- 7.
- A. Cauchy, Mémoire sur les systèmes d'equations aux dérivées partielles d'ordres quelconques, et sur leur réduction à des systèmes d'equations linéaires du premier ordre, C. .R. Acad. Sci. Paris 15 (1842), 131.
- 8.
- J. Chazarain and A. Piriou, Introduction to the theory of linear partial differential equations, North-Holland, Amsterdam, 1982. MR 678605
- 9.
- G. Folland, Lectures on partial differential equations, Tata Institute of Fundamental Research, Springer-Verlag, Berlin and New York, 1983. MR 696577
- 10.
- M. Gevrey, Sur les équations aux dérivées partielles du type parabolique, J. Math. Pures Appl. 9(6) (1913), 305-475.
- 11.
- M. Gevrey, Sur les fonctions indéfinement dérivables de classe donnée et leur rôle dans la théorie des équations partielles, C. R. Acad. Sci. Paris 157 (1913), 1121-1124.
- 12.
- J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Yale Univ. Press, New Haven, CT, 1923.
- 13.
- E. Holmgren, Über Systeme von linearen partiellen Differentialgleichungen, Öfversigt af Kongl. Vetenskap-Akad. Förh. 58 (1901), 91-103.
- 14.
- L. Hörmander, Pseudo-differential operators and hypoelliptic equations, Proc. Sympos. Pure Math., vol. 10, Amer. Math. Soc., Providence, R. I., 1967, pp. 138-183. MR 383152
- 15.
- L. Hörmander, Linear differential operators, Actes Congr. Int. Math. Nice 1 (1970), 121-133. MR 513000
- 16.
- L. Hörmander, The analysis of linear partial differential operators, vols. I-IV, Springer-Verlag, Berlin and New York, 1983-1985. MR 717035
- 17.
- J. J. Kohn and L. Nirenberg, An algebra of pseudo-differential operators, Comm. Pure Appl. Math. 18 (1965), 269-305. MR 176362
- 18.
- S. Kowalevsky, Zur Theorie der partiellen Differentialgleichungen, J. Reine Angew. Math. 80 (1875), 1-32.
- 19.
- P. D. Lax, Asymptotic solutions of oscillatory initial value problems, Duke Math. J. 24 (1957), 627-646. MR 97628
- 20.
- S. G. Mihlin, On the multipliers of Fourier integrals, Dokl. Akad. Nauk SSSR 109 (1956), 701-703. (Russian) MR 80799
- 21.
- S. Mizohata, Some remarks on the Cauchy problem, J. Math. Kyoto Univ. 1 (1961), 109-127. MR 170112
- 22.
- I. G. Petrowsky, Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen, Mat. Sb. 2(44) (1937), 815-870.
- 23.
- I. G. Petrowsky, Über das Cauchysche Problem für ein System linearer partieller Differentialgleichungen im Gebiete der nichtanalytischen Funktionen, Bull. Univ. Moscow Ser. Int. 1(7) (1938), 1-74.
- 24.
- M. Sato, Regularity of hyperfunction solutions of partial differential equations, Actes Congr. Int. Math. Nice 2 (1970), 785-794. MR 650826
- 25.
- M. Taylor, Pseudodifferential operators, Princeton Univ. Press, Princeton, N. J., 1981. MR 618463
- 26.
- F. Treves, Introduction to pseudodifferential and Fourier integral operators. Vol. I: Pseudodifferential operators; Vol. 2: Fourier integral operators, Plenum Press, New York, 1980. MR 597145
Additional Information:
Reviewer(s):
Michael
Beals
Review Information:
Journal:
Bull. Amer. Math. Soc.
17
(1987),
169-176.
DOI:
10.1090/S0273-0979-1987-15552-2
PII:
S 0273-0979(1987)15552-2
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