On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I : derivation of necessary conditions
Annales de l'I.H.P. Physique théorique, Volume 20 (1974) no. 2, p. 153-188
@article{AIHPA_1974__20_2_153_0,
     author = {McLenaghan, R. G.},
     title = {On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I : derivation of necessary conditions},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {20},
     number = {2},
     year = {1974},
     pages = {153-188},
     zbl = {0287.35058},
     mrnumber = {361452},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1974__20_2_153_0}
}
McLenaghan, R. G. On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I : derivation of necessary conditions. Annales de l'I.H.P. Physique théorique, Volume 20 (1974) no. 2, pp. 153-188. http://www.numdam.org/item/AIHPA_1974__20_2_153_0/

[1] L. Asgeirsson, Some hints on Huygens' principle and Hadamard's conjecture. Comm. Pure Appl. Math., t. 9, 1956, p. 307. | MR 82034 | Zbl 0074.31101

[2] Y. Bruhat, Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires. Acta Math., t. 88, 1952, p. 141. | MR 53338 | Zbl 0049.19201

[3] M. Cahen and R. Mclenaghan, Métriques des espaces lorentziens symétriques à quatre dimensions. C. R. Acad. Sci. Paris, t. 266, 1968, p. 1125. | MR 231326 | Zbl 0172.27904

[4] M. Chevalier, Sur le noyau de diffusion de l'opérateur laplacien. C. R. Acad. Sci. Paris, t. 264, 1967, p. 380. | MR 226555

[5] E. Cotton, Sur les invariants différentiels de quelques équations linéaires aux dérivées partielles du second ordre. Ann. Sc. Ec. Norm. Supérieure, t. 17, 1900, p. 211. | JFM 31.0379.02 | Numdam | MR 1508982

[6] R. Courant and D. Hilbert, Methods of mathematical physics, t. 2, Interscience, New York, 1962. | Zbl 0099.29504

[7] A. Douglis, The problem of Cauchy for linear hyperbolic equations of second order. Comm. Pure Appl. Math., t. 7, 1954, p. 271. | MR 62931 | Zbl 0059.08801

[8] A. Douglis, A criterion for the validity of Huygens' principle. Comm. Pure Appl. Math., t. 9, 1956, p. 391. | MR 82035 | Zbl 0075.09701

[9] J.C. Du Plessis, Polynomial conformal tensors. Proc. Cambridge Philos. Soc., t. 68, 1970, p. 329. | MR 259802 | Zbl 0203.54603

[10] F.G. Friedlander, The wave equation in a curved space-time. Cambridge University Press (to appear). | MR 460898 | Zbl 0316.53021

[11] P. Günther, Zur Gültigkeit des Huygensschen Princips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus. S.-B. Sachs. Akad. Wiss. Leipzig Math.-Natur. Kl., t. 100, 1952, p. 1. | MR 50136 | Zbl 0046.32201

[12] P. Günther, Uber einige spezielle Probleme aus der Theorie der linearen partiellen Differentialgleichungen zweiter Ordnung. S.-B. Sachs. Akad. Wiss. Leipzig Math.- Natur. Kl., t. 102, 1957, p. 1. | MR 109937 | Zbl 0085.08202

[13] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differentialgleichungen mit vier unabhängigen Variablen. Arch. Rational Mech. Anal., t. 18, 1965, p. 103. | MR 174865 | Zbl 0125.05404

[14] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations. Yale University Press, New Haven, 1923. | JFM 49.0725.04

[15] J. Hadamard, The problem of diffusion of waves. Ann. of Math., t. 43, 1942, p. 510. | MR 6809 | Zbl 0063.01841

[16] S. Helgason, Lie Groups and Symmetric Spaces. Article in Batelle Recontres 1967, lectures in mathematics and physics. W. A. Benjamin, Inc., New York, 1968. | MR 236325 | Zbl 0177.50601

[17] G. Herglotz, Uber die Bestimmung eines Linienelementes in normal Koorinaten aus dem Riemannschen Krümmgstensor. Math. Ann., t. 93, 1925, p. 46. | JFM 50.0492.07 | MR 1512221

[18] J. Leray, Hyperbolic Partial Differential Equations. Mimeographed Notes, Institute of Advanced Study, Princeton.

[19] A. Lichnerowicz, Propagateurs et commutateurs en relativité générale. Publ. Math. I. H. E. S., n° 10, 1961, p. 293. | Numdam | MR 158726 | Zbl 0098.42607

[20] D. Lovelock, The Lanczos identity and its generalizations. Atti. Accad. Naz. Lincei, t. 42, 1967, p. 187. | MR 216427 | Zbl 0194.22802

[21] M. Mathisson, Eine Lösungsmethode fur Differentialgleichungen vom normalen hyperbolischen Typus. Math. Ann., t. 107, 1932, p. 400. | JFM 58.1561.01

[22] M. Mathisson, Le problème de M. Hadamard relatif à la diffusion des ondes. Acta. Math., t. 71, 1939, p. 249. | MR 728 | Zbl 0022.22802

[23] R.G. Mclenaghan, An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle. Proc. Cambridge Philos. Soc., t. 65, 1969, p. 139. | MR 234700 | Zbl 0182.13403

[24] R. Penrose, A spinor approach to general relativity. Ann. Physics, t. 10, 1960, p. 171. | MR 115765 | Zbl 0091.21404

[25] A.Z. Petrov, Einstein-Räume. Akademie Verlag, Berlin, 1964. | MR 162594 | Zbl 0114.21003

[26] H.S. Ruse, A.G. Walker and T.J. Willmore, Harmonic Spaces. Edizioni Cremonese, Rome, 1961. | MR 142062 | Zbl 0134.39202

[27] J.A. Schouten, Ricci-Calculus. Springer-Verlag, Berlin, 1954. | MR 516659 | Zbl 0057.37803

[28] S.L. Sobolev, Méthode nouvelle à résoudre le problème de Cauchy pour les équations linéaires hyperboliques normales. Mat. Sb. (N. S.), t. 1, 1936, p. 39. | JFM 62.0568.01 | Zbl 0014.05902

[29] K.L. Stellmacher, Ein Beispiel einer Huygensschen Differentialgleichung. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II, t. 10, 1953, p. 133. | MR 60695 | Zbl 0052.09901

[30] K.L. Stellmacher, Eine Klasse huygenscher Differentialgleichungen und ihre Integration. Math. Ann., t. 130, 1955, p. 219. | MR 73831 | Zbl 0134.31101

[31] P. Szekeres, Conformal Tensors. Proc. Roy. Soc. London, A, t. 304, 1968, p. 113. | Zbl 0159.23903

[32] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhangigen Variablen. Math. Nachr., t. 47, 1970, p. 131. | MR 298221 | Zbl 0211.40803