Huygens' principle
Annales de l'I.H.P. Physique théorique, Volume 37 (1982) no. 3, p. 211-236
@article{AIHPA_1982__37_3_211_0,
     author = {McLenaghan, R. G.},
     title = {Huygens' principle},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     publisher = {Gauthier-Villars},
     volume = {37},
     number = {3},
     year = {1982},
     pages = {211-236},
     zbl = {0528.35057},
     mrnumber = {694586},
     language = {en},
     url = {http://www.numdam.org/item/AIHPA_1982__37_3_211_0}
}
McLenaghan, R. G. Huygens' principle. Annales de l'I.H.P. Physique théorique, Volume 37 (1982) no. 3, pp. 211-236. http://www.numdam.org/item/AIHPA_1982__37_3_211_0/

[1] L. Asgeirsson, Some hints on Huygen's principle and Hadamard's conjecture. Comm. Pure Appl. Math., t. 9, 1956, p. 307-326. | MR 82034 | Zbl 0074.31101

[2] R. Bach, Zur Weylshcen Relativitats theorie. Math. Zeitscher, t. 9, 1921, p. 110- 135. | JFM 48.1035.01 | MR 1544454

[3] Y. Bruhat, Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires. Acta Math., t. 88, 1952, p. 141-225. | MR 53338 | Zbl 0049.19201

[4] M. Cahen, R. Debever and L. Defrise, A Complex vectorial formalism in general relativity, J. Math. Mech., t. 16, 1967, p. 761-786. | MR 207370 | Zbl 0149.23401

[5] M. Cahen and R. Mclenaghan, Métriques des espaces lorentziens symétriques à quatre dimensions. C. R. Acad. Sci. Paris, t. 266, 1968, p. 1125-1128. | MR 231326 | Zbl 0172.27904

[6] M. Chevalier, Sur le noyau de diffusion de l'opérateur laplacien. C. R. Acad. Sci. Paris, T. 264, 1967, p. 380-382. | MR 226555

[7] E. Cotton, Sur les invariants différentials de quelques équations linéaires aux dérivées partielles du second ordre. Ann. Sc. Ec. Norm. Superieure, t. 17, 1900, p. 211-244. | JFM 31.0379.02 | Numdam | MR 1508982

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

[9] R. Debever, Le rayonnement gravitationnel, le tenseur de Riemann en relativité générale. Cah. Phys., t. 168-169, 1964, p. 303-349. | MR 187877

[10] A. Douglis, The problem of Cauchy for linear hyperbolic equations of second order. Comm. Pure Appl. Math., t. 7, 1954, p. 271-295. | MR 62931 | Zbl 0059.08801

[11] A. Douglis, A criterion for the validity of Huygens' principle. Comm. Pure Appl. Math., t. 9, 1956, p. 391-402. | MR 82035 | Zbl 0075.09701

[12] J.C. Du Plessis, Polynomial conformal tensors. Proc. Cambridge Philos. Soc., t. 68, 1970, p. 329-344. | MR 259802 | Zbl 0203.54603

[13] J. Ehlers and K. Kundt, Exact solutions of the gravitational Field equations. Article in Gravitation an introduction to current research ; edited by L. Witten, Wiley, New York, 1964.

[14] F.G. Friedlander, The wave equation in a curved space-time. Cambridge University Press, Cambridge, 1975. | MR 460898 | Zbl 0316.53021

[15] R. Goldoni. A necessary condition for the validity of Huygen's principle on a curved space-time, J. Math. Phys., 18, 1977, p. 2125-2128. | MR 484227 | Zbl 0366.35053

[16] P. Günther, Zur Gültigkeit des Huygensschen Princips bei partiellen Differentialgleichungen von normalen hyperbolischen Typus. S.-B. Sächs. Akad. Wiss. Leipzig Math.-Natur. Kl., t. 100, 1952, p. 1-43. | MR 50136 | Zbl 0046.32201

[17] P. Günther, Über einige spezielle Probleme aus der Theorie der Linearen partiellen Differentialgleichungen zweiter Ordnung. S.-B. Sächs. Akad. Wiss. Leipzig Math.-Natur. Kl., t. 102, 1957, p. 1-50. | MR 109937 | Zbl 0085.08202

[18] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differentialgleichungen mit vier unabhängigen Variablen. Arch. Rational Mech. Anal., t. 18, 1965, p. 103- 106. | MR 174865 | Zbl 0125.05404

[19] P. Günther, Einige Sätze über huygenssche Differentialgleichungen. Wiss. Zeitschr. Karl Marx Univ., Math.-natu. Reihe Leipzig, t. 14, 1965, p. 497-507. | MR 198012 | Zbl 0173.12203

[20] P. Günther and V. Wünsch, Maxwellsche Gleichungen und Huygensshes. Prinzip I. Math. Nach., 63, 1974, p. 97-121. | MR 363377 | Zbl 0288.35042

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

[22] J. Hadamard, The problem of diffusion of waves. Ann. of Math., t. 43, 1942, p. 510-522. | MR 6809 | Zbl 0063.01841

[23] G. Herglotz, Über die Bestimmung eines Linienelementes in normal Koorinaten aus dem Riemannschen Krümmgstensor, Math. Ann., t. 93, 1925, p. 46-53. | JFM 50.0492.07 | MR 1512221

[24] E. Hölder, Poissonsche Wellenformel in nicht euclidischen Raumen. Ber. Verh. Sachs. Akad. Wiss. Leipzig, t. 99, 1938, p. 53-66. | JFM 64.1174.02 | Zbl 0019.26101

[25] N.H. Ibragimov and E.V. Mamontov, Sur le problème de J. Hadamard relatif à la diffusion des ondes. C. R. Acad. Sc. Paris, t. 270, 1970, p. 456-458. | MR 257567 | Zbl 0196.12004

[26] N.H. Ibragimov, Huygens' principle. Amer. Math. Soc. Transl. (2), t. 104, 1976, p. 141-151. | Zbl 0327.35008

[27] N.H. Ibragimov and E.V. Mamontov, On the Cauchy problem for the equation Utt - Uxx - ∑aij(x - t)Uyiyj = 0. Math. Sbornik Tom, t. 102 (144), 1977, N° 3, p. 347-363. | MR 440207 | Zbl 0386.35027

[28] H.P. Künzle, Maxwell Fields satisfying Huygens' principle. Proc. Cambridge Philos. Soc., t. 64, 1968, p. 779-785.

[29] A. Lichnerowicz, Propagateurs et commutateurs en relativité générale. Publ. Math. I. H. E. S., t. 10, 1961, p. 293-344. | Numdam | MR 158726 | Zbl 0098.42607

[30] M. Mathisson, Eine Lösungsmethode fur Differentialgleichungen vom normalen hyperbolischen Typus. Math. Ann., t. 107, 1932, p. 400-419. | JFM 58.1561.01

[31] M. Mathisson, Le problème de M. Hadamard relatif à la diffusion des ondes. Acta Math., t. 71, 1939, p. 249-282. | MR 728 | Zbl 0022.22802

[32] 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. 139-155. | MR 234700 | Zbl 0182.13403

[33] R.G. Mclenaghan, On the validity of Huygens' principle for second order partial differential equations with four independent variables. Part I: Derivation of necessary conditions. Ann. Inst. Henri Poincaré, t. A 20, 1974, p. 153-188. | Numdam | MR 361452 | Zbl 0287.35058

[34] R.G. Mclenaghan and J. Leroy, Complex recurrent space-times. Proc. Roy. Soc. London, t. A 327. 1972, p. 229-249. | MR 309517 | Zbl 0243.53030

[35] R. Penrose, A spinor approach to general relativity, Ann. Physics, t. 10, 1960, p. 171-201. | MR 115765 | Zbl 0091.21404

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

[37] F.A.E. Pirani, Introduction to gravitational radiation theory. Article in Lectures on General Relativity, edited by S. Deser and W. Ford, Brandeis Summer Institute in Theoretical Physics, t. 1. 1964. Prentice-Hall, New York.

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

[39] R. Schimming, Zur Gültiakeit des huygensschen Prinzips bei einer speziellen Metrik, Z. A. M. M., t. 51, 1971, p. 201-208. | MR 290313 | Zbl 0221.35011

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

[41] 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. 39-70. | JFM 62.0568.01 | Zbl 0014.05902

[42] K.L. Stellmacher. Ein Beispiel einer Huygensschen Differentialgleichung. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl., II. t. 10. 1953, p. 133-138. | MR 60695 | Zbl 0052.09901

[43] K.L. Stellmacher, Eine Klasse huygenscher Differentialgleichungen und ihre Integration. Math. Ann., t. 130, 1955, p. 219-233. | MR 73831 | Zbl 0134.31101

[44] P. Szekeres, Spaces conformal to a class of spaces in general relativity. Proc. Roy. Soc. London, t. A 274, 1963, p. 206-212. | MR 158729 | Zbl 0113.44805

[45] P. Szekeres, Conformal Tensors. Proc. Roy. Soc. London, t. A 304, 1968, p. 113-122. | Zbl 0159.23903

[46] G. Vandercappellen, Contributions à l'étude du principle d'Huygens' en espace temps courbe. Mémoire de Licence, Université de l'État à Mons, 1980.

[47] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen. Math. Nachr., t. 47, 1970, p. 131-154. | MR 298221 | Zbl 0211.40803

[48] V. Wünsch, Maxwellsche Gleichungen und Huygensches II. Math. Nach., t. 73, 1976, p. 19-36. | MR 426807 | Zbl 0288.35043

[49] V. Wünsch, Über eine Klasse Konforminvarianter Tensoren. Math. Nach., t. 73, 1976, p. 37-58. | MR 433342 | Zbl 0287.53014

[50] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen I. Beitr. zur Analysis, t. 12, 1978, p. 47-76. | MR 507097 | Zbl 0448.58022

[51] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichunger II. Beitr. zur Analysis, t. 13, 1979, p. 147-177. | MR 536225 | Zbl 0467.35067