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On Cauchy’s problem for hyperbolic equations and the differentiability of solutions of elliptic equations. (English) Zbl 0067.07502


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[1] Courant, Math. Ann. 100 pp 32– (1928)
[2] Sur quelques évaluations concernant les familles des fonctions ayant des dérivées à carré intégrable, C. R. Acad. Sci. S. S.S. R., N. S. L. 1936, pp. 279–282. · JFM 62.0266.01
[3] and , Methoden der mathematischen Physik, Vol. II, Chapt. VII, Springer, Berlin, 1937. · Zbl 0017.39702 · doi:10.1007/978-3-642-47434-7
[4] On a theorem of functional analysis, Mat. Sbornik, N. S. 4, 1938, pp. 471–497.
[5] Friedrichs, Amer. J. Math. pp 523– (1939)
[6] Petrowsky, Recueil mathématique, N. S. (Mat. Sbornik) 5 pp 3– (1939)
[7] Friedrichs, Trans. Amer. Math. Soc. 55 pp 132– (1944)
[8] Friedrichs, Duke Math. J. 14 pp 67– (1947)
[9] Van Hove, Indagationes Math. 7 pp 3– (1947)
[10] Acad. Roy. Belgique, Cl. Sci., Mém. 24 (1949)
[11] The method of orthogonal and direct decomposition in the theory of elliptic differential equations, Mat. Sbornik, N. S. 25, 1949, pp. 189–234.
[12] Théorie des distributions, Paris, Hermann, 1950–1951. · Zbl 0050.11402
[13] Gårding, C. R. Acad. Sci. Paris 230 pp 1030– (1950)
[14] Vishik, Akad. Nauk, S. S.S. R., Doklady 74 pp 881– (1950)
[15] (B) Mat. Sbornik, N. S. 29, 1951, pp. 615–676.
[16] General properties of solutions of linear elliptic partial differential equations Proc. of the Symposium on Spectral Theory and Differential Problems, Stillwater, Oklahoma, 1951, Chap. III.
[17] Gåding, C. R. Acad. Sci. Paris 233 pp 1554– (1951)
[18] Milgram, Proc. Nat. Acad. Sci. 37 pp 180– (1951)
[19] Browder, Proc. Nat. Acad. Sci. 38 pp 230– (1952)
[20] (B) The Dirichlet and vibration problems for linear elliptic differential equations of arbitrary order, Vol. 38, No. 8, 1952, pp. 741–747. · Zbl 0047.09501
[21] (C) Assumption of boundary values and the Green’s function in the Dirichlet problem for the general linear elliptic equation, Vol. 39, No. 3, 1953, pp. 179–184. · Zbl 0050.09701
[22] (D) Linear parabolic differential equations of arbitrary order: general boundary-value problems for elliptic equations, Vol. 39, No. 3, 1953, pp. 185–190. · Zbl 0050.09702
[23] John, Comm. Pure Appl. Math. pp 327– (1953)
[24] Strongly elliptic systems of differential equations, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, No. 33, Princeton Univ. Press, 1954, pp. 15–51.
[25] and , Parabolic equations, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, No. 33, Princeton Univ. Press, 1954, pp. 167–190.
[26] Second order elliptic system of differential equations, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, No. 33, Princeton Univ. Press, 1954, pp. 101–159.
[27] Weber, Braunschweig, Friedrich Vieweg 1 pp 390– (1900)
[28] Hadamard, Bull. Soc. Math. France 28 pp 69– (1900)
[29] Zaremba, Rend. Accad. Naz. Lincei, Ser. 5 24 pp 904– (1915)
[30] Rubinowicz, Monatsh. Math. Phys. 30 pp 65– (1920)
[31] Phys. Zeit. 27 pp 707– (1926)
[32] Math. Ann. 96 pp 648– (1927)
[33] Friedrichs, Math. Ann. 98 pp 192– (1927)
[34] (B) Über fortsetzbare Anfangsbedingungen bei hyperbolischen Differentialgleichungen in drei Veränderlichen, Nachr. Ges. Wiss. Göttingen, No. 26, 1932, pp. 135–143. · Zbl 0004.35002
[35] Schauder, Fund. Math. 24 pp 213– (1935)
[36] Sobolev, Akad. Nauk, SSSR, Trudy Mat. Inst. V. A. Steklova 9 pp 39– (1935)
[37] (B) Méthode nouvelle å résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales, Rec. Math. (Mat. Sbornik), N. S. 1(43), 1936, pp. 39–72.
[38] über das Anfangswertproblem füx lineare und nichtlineare hyperbolische partielle Differentialgleichungen zweiter Ordnung, Rec. Math. (Mat. Sbornik), N. S. 2(44), 1937, pp. 793–814. · JFM 63.0469.01
[39] Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen, Rec. Math. (Mat. Sbornik), N. S. 2(44), 1937, pp. 814–868. · Zbl 0018.40503
[40] Sur la théorie des équations hyperboliques aux dérivées partielles, Rec. Math. (Mat. Sbornik), N. S. 5(47), 1939, pp. 71–99.
[41] (A) Lectures on hyperbolic equations with variable coefficients, Princeton, Inst. for Adv. Stud., Fall, 1952.
[42] (B) On linear hyperbolic differential equations with variable coefficients on vectir soaces, Annals of Mathematics Studies, No. 33, Princeton Univ. Press, 1954, pp. 201–210.
[43] Holmgren, Öfvere. Kongl. Vetens.-Akad. Förh. 58 pp 91– (1901)
[44] Lectures on Cauchy’s problem in linear partial differential equations, Yale Univ. Press, 1923, or · JFM 49.0725.04
[45] Le Probléme de Cauchy et les équations aux dérivées partielles linéires hyperboliques, Hermann, Paris, 1932.
[46] Riesz, Acta Math. 81 pp 1– (1948)
[47] Quelques questions de Géométrie suggétrie par la théorie dea équations aux dérivées partielles totalement hyperboliques, Colloque de Géométrie Algébrique, Liege, 1949.
[48] Weyl, Duke Math. J. 7 pp 411– (1940)
[49] Gårding, Kungl. Fys. Sällskapets i Lund Förh. 20 pp 1– (1950)
[50] Courant, Bull. Amer. Math. Soc. 49 pp 1– (1943)
[51] Gårding, C. R. Acad. Sci. Paris 239 pp 849– (1954)
[52] Remarks on strongly elliptic partial differential equations, appearing in this issue.
[53] Friedrichs, Comm. Pure and Appl. Math. 6 pp 299– (1953)
[54] Friedrichs, Comm. Pure and Appl. Math. 7 pp 345– (1954)
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