Huygens' principle

 Access to full text

 Full (PDF)

1. [1] L. Asgeirsson, Some hints on Huygen's principle and Hadamard's conjecture. Comm. Pure Appl. Math., t. 9, 1956, p. 307-326. Zbl0074.31101MR82034
2. [2] R. Bach, Zur Weylshcen Relativitats theorie. Math. Zeitscher, t. 9, 1921, p. 110- 135. MR1544454JFM48.1035.01
3. [3] Y. Bruhat, Théorème d'existence pour certains systèmes d'équations aux dérivées partielles non linéaires. Acta Math., t. 88, 1952, p. 141-225. Zbl0049.19201MR53338
4. [4] M. Cahen, R. Debever and L. Defrise, A Complex vectorial formalism in general relativity, J. Math. Mech., t. 16, 1967, p. 761-786. Zbl0149.23401MR207370
5. [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. Zbl0172.27904MR231326
6. [6] M. Chevalier, Sur le noyau de diffusion de l'opérateur laplacien. C. R. Acad. Sci. Paris, T. 264, 1967, p. 380-382. MR226555
7. [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. Zbl31.0379.02MR1508982JFM31.0379.02
8. [8] R. Courant and D. Hilbert, Methods of mathematical physics, vol. 2, Interscience, New York, 1962. Zbl0099.29504
9. [9] R. Debever, Le rayonnement gravitationnel, le tenseur de Riemann en relativité générale. Cah. Phys., t. 168-169, 1964, p. 303-349. MR187877
10. [10] A. Douglis, The problem of Cauchy for linear hyperbolic equations of second order. Comm. Pure Appl. Math., t. 7, 1954, p. 271-295. Zbl0059.08801MR62931
11. [11] A. Douglis, A criterion for the validity of Huygens' principle. Comm. Pure Appl. Math., t. 9, 1956, p. 391-402. Zbl0075.09701MR82035
12. [12] J.C. Du Plessis, Polynomial conformal tensors. Proc. Cambridge Philos. Soc., t. 68, 1970, p. 329-344. Zbl0203.54603MR259802
13. [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. [14] F.G. Friedlander, The wave equation in a curved space-time. Cambridge University Press, Cambridge, 1975. Zbl0316.53021MR460898
15. [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. Zbl0366.35053MR484227
16. [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. Zbl0046.32201MR50136
17. [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. Zbl0085.08202MR109937
18. [18] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differentialgleichungen mit vier unabhängigen Variablen. Arch. Rational Mech. Anal., t. 18, 1965, p. 103- 106. Zbl0125.05404MR174865
19. [19] P. Günther, Einige Sätze über huygenssche Differentialgleichungen. Wiss. Zeitschr. Karl Marx Univ., Math.-natu. Reihe Leipzig, t. 14, 1965, p. 497-507. Zbl0173.12203MR198012
20. [20] P. Günther and V. Wünsch, Maxwellsche Gleichungen und Huygensshes. Prinzip I. Math. Nach., 63, 1974, p. 97-121. Zbl0288.35042MR363377
21. [21] J. Hadamard, Lectures on Cauchy's problem in linear partial differential equations. Yale University Press, New Haven, 1923. Zbl49.0725.04JFM49.0725.04
22. [22] J. Hadamard, The problem of diffusion of waves. Ann. of Math., t. 43, 1942, p. 510-522. Zbl0063.01841MR6809
23. [23] G. Herglotz, Über die Bestimmung eines Linienelementes in normal Koorinaten aus dem Riemannschen Krümmgstensor, Math. Ann., t. 93, 1925, p. 46-53. MR1512221JFM50.0492.07
24. [24] E. Hölder, Poissonsche Wellenformel in nicht euclidischen Raumen. Ber. Verh. Sachs. Akad. Wiss. Leipzig, t. 99, 1938, p. 53-66. Zbl0019.26101JFM64.1174.02
25. [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. Zbl0196.12004MR257567
26. [26] N.H. Ibragimov, Huygens' principle. Amer. Math. Soc. Transl. (2), t. 104, 1976, p. 141-151. Zbl0327.35008
27. [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. Zbl0386.35027MR440207
28. [28] H.P. Künzle, Maxwell Fields satisfying Huygens' principle. Proc. Cambridge Philos. Soc., t. 64, 1968, p. 779-785. 
29. [29] A. Lichnerowicz, Propagateurs et commutateurs en relativité générale. Publ. Math. I. H. E. S., t. 10, 1961, p. 293-344. Zbl0098.42607MR158726
30. [30] M. Mathisson, Eine Lösungsmethode fur Differentialgleichungen vom normalen hyperbolischen Typus. Math. Ann., t. 107, 1932, p. 400-419. Zbl58.1561.01JFM58.1561.01
31. [31] M. Mathisson, Le problème de M. Hadamard relatif à la diffusion des ondes. Acta Math., t. 71, 1939, p. 249-282. Zbl0022.22802MR728
32. [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. Zbl0182.13403MR234700
33. [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. Zbl0287.35058MR361452
34. [34] R.G. Mclenaghan and J. Leroy, Complex recurrent space-times. Proc. Roy. Soc. London, t. A 327. 1972, p. 229-249. Zbl0243.53030MR309517
35. [35] R. Penrose, A spinor approach to general relativity, Ann. Physics, t. 10, 1960, p. 171-201. Zbl0091.21404MR115765
36. [36] A.Z. Petrov, Einstein-Raume, Akademie Verlag, Berlin, 1964. Zbl0114.21003MR162594
37. [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. [38] H.S. Rlse. A.G. Walker and T.J. Willmore, Harmonic Spaces, Edizioni Cremonese. Rome. 1961. Zbl0134.39202MR142062
39. [39] R. Schimming, Zur Gültiakeit des huygensschen Prinzips bei einer speziellen Metrik, Z. A. M. M., t. 51, 1971, p. 201-208. Zbl0221.35011MR290313
40. [40] J.A. Schouten, Ricci-Calculus, Springer-Verlag, Berlin, 1954. Zbl0057.37803MR516659
41. [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. Zbl0014.05902JFM62.0568.01
42. [42] K.L. Stellmacher. Ein Beispiel einer Huygensschen Differentialgleichung. Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl., II. t. 10. 1953, p. 133-138. Zbl0052.09901MR60695
43. [43] K.L. Stellmacher, Eine Klasse huygenscher Differentialgleichungen und ihre Integration. Math. Ann., t. 130, 1955, p. 219-233. Zbl0134.31101MR73831
44. [44] P. Szekeres, Spaces conformal to a class of spaces in general relativity. Proc. Roy. Soc. London, t. A 274, 1963, p. 206-212. Zbl0113.44805MR158729
45. [45] P. Szekeres, Conformal Tensors. Proc. Roy. Soc. London, t. A 304, 1968, p. 113-122. Zbl0159.23903
46. [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. [47] V. Wünsch, Über selbstadjungierte Huygenssche Differentialgleichungen mit vier unabhängigen Variablen. Math. Nachr., t. 47, 1970, p. 131-154. Zbl0211.40803MR298221
48. [48] V. Wünsch, Maxwellsche Gleichungen und Huygensches II. Math. Nach., t. 73, 1976, p. 19-36. Zbl0288.35043MR426807
49. [49] V. Wünsch, Über eine Klasse Konforminvarianter Tensoren. Math. Nach., t. 73, 1976, p. 37-58. Zbl0287.53014MR433342
50. [50] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichungen I. Beitr. zur Analysis, t. 12, 1978, p. 47-76. Zbl0448.58022MR507097
51. [51] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen Klassen spinorieller Feldgleichunger II. Beitr. zur Analysis, t. 13, 1979, p. 147-177. Zbl0467.35067MR536225

1. J. Carminati, R. G. McLenaghan, An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. — Part II : Petrov type D space-times
2. J. Carminati, R. G. McLenaghan, An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times
3. V. Wünsch, Huygens' principle on Petrov type N space-times
4. W. G. Anderson, R. G. McLenaghan, F. D. Sasse, Huygens' principle for the non-self-adjoint scalar wave equation on Petrov type III space-times
5. V. Wünsch, Moments and Huygens' principle for conformally invariant field equations in curved space-times
6. R. G. McLenaghan, T. F. Walton, An explicit determination of the non-self-adjoint wave equations on curved space-time that satisfy Huygens' principle. Part I : Petrov type N background space-times
7. J. Carminati, R. G. McLenaghan, An explicit determination of the Petrov type N space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle