On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition
Annales de l'I.H.P. Physique théorique, Volume 60 (1994) no. 4, pp. 373-432.
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     author = {Anderson, W. G. and McLenaghan, R. G.},
     title = {On the validity of {Huygens'} principle for second order partial differential equations with four independent variables. {II.} {A} sixth necessary condition},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     pages = {373--432},
     publisher = {Gauthier-Villars},
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     year = {1994},
     mrnumber = {1288586},
     zbl = {0806.35104},
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     url = {http://archive.numdam.org/item/AIHPA_1994__60_4_373_0/}
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Anderson, W. G.; McLenaghan, R. G. On the validity of Huygens' principle for second order partial differential equations with four independent variables. II. A sixth necessary condition. Annales de l'I.H.P. Physique théorique, Volume 60 (1994) no. 4, pp. 373-432. http://archive.numdam.org/item/AIHPA_1994__60_4_373_0/

[1] W.G. Anderson, Contributions to the Study of Huygens' Principle for the Non-self-adjoint Scalar Wave Equation on Curved Space-time, M. Math. Thesis (unpublished), University of Waterloo, 1991.

[2] W.G. Anderson, R.G. Mclenaghan and T.F. Walton, An Explicit Determination of the Non-Self-Adjoint Wave Equations on Curved Space-Time that Satisfy Huygens' Principle. Part II: Petrov Type III Background Space-Times, submitted to Ann. Inst. Henri Poincaré, Phys. Théor.

[3] W.G. Anderson and R.G. Mclenaghan, On Huygens' Principle for Relativistic Wave Equations, C. R. Math. Rep. Acad. Sci. Canada XV, 1993, p. 41. | MR | Zbl

[4] L. Asgeirsson, Some Hints on Huygens' Principle and Hadamard's Conjecture, Comm. Pure Appl. Math., 9, 1956, p. 307. | MR | Zbl

[5] J. Carminati, S.R. Czapor, R.G. Mclenaghan and G.C. Williams, Consequences of the Validity of Huygens' Principle for the Conformally Invariant Scalar Wave Equation, Weyl's Neutrino Equation and Maxwell's Equations on Petrov Type II Space-Times, Ann. Inst. Henri Poincaré, Phys. Théor., 54, 1991, p. 9. | Numdam | Zbl

[6] J. Carminati and R.G. Mclenaghan, An Explicit Determination of the Petrov Type N Space-times on which the Conformally Invariant Scalar Wave Equation Satisfies Huygens' Principle, Ann. Inst. Henri Poincaré, Phys. Théor., 44, 1986, p. 115. | Numdam | MR | Zbl

[7] J. Carminati and 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, Ann. Inst. Henri Poincaré, Phys. Théor., 47, 1987, p. 337. | Numdam | MR | Zbl

[8] J. Carminati and 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, Ann. Inst. Henri Poincaré, Phys. Théor., 48, 1988, p. 77. | Numdam | MR | Zbl

[9] J. Ehlers and K. Kundt, Exact Solutions of the Gravitational Field Equations, Chapter 2 of Gravitation an Introduction to Current Research, L. Witten editor, John Wiley and Sons, Toronto, 1962. | MR

[10] F.G. Friedlander, The Wave Equation on a Curved Space-Time, Cambridge University Press, London, 1976. | MR | Zbl

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

[12] P. Günther, Ein Beispiel einer nichttrivalen Huygensschen Differential-gleichungen mit vier unabhängigen Variablen, Arch. Ration. Mech. Anal., 18, 1965, p. 103. | MR | Zbl

[13] P. Günther and V. Wünsch, Maxwellsche Gleichungen und Huygenssches Prinzip I, Math. Nach., 63, 1974, p. 97. | MR | Zbl

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

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

[16] G. Herglotz, Uber die Bestimmung eines Linienelementes in normal Koordinaten aus dem Riemannschen Krümmgstensor, Math. Ann., 93, 1925, p. 46. | JFM | MR

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

[18] M. Mathisson, Le problème de M. Hadamard relatif à la diffusion des ondes, Acad. Math., 71, 1939, p. 249. | MR | Zbl

[19] R.G. Mclenaghan, An Explicit Determination of the Empty Space-times on which the Wave Equation Satisfies Huygens' Principle, Proc. Cambridge Philos. Soc., 65, 1969, p. 139. | MR | Zbl

[20] R.G. Mclenaghan, On the Validity of Huygen's Principle for Second Order Partial Differential Equations with four Independent Variables, Part I: Derivation of Necessary Conditions, Ann. Inst. Henri Poincaré, A20, 1974, p. 153. | Numdam | MR | Zbl

[21] R.G. Mclenaghan and 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, Ann. Inst. Henri Poincaré, Phys. Théor., 48, 1988, p. 267. | Numdam | MR | Zbl

[22] R.G. Mclenaghan and G.C. Williams, An Explicit Determination of the Petrov Type D Space-Times on which Weyl's Neutrino Equation and the Maxwell's Equations Satisfy Huygens' Principle, Ann. Inst. Henri Poincaré, Phys. Théor., 53, 1990, p. 217. | Numdam | Zbl

[23] B. Rinke and V. Wünsch, Zum Huygensschen Prinzip bei der skalaren Wellengleichung, Beitr. zur Analysis, 18, 1981, p. 43. | MR | Zbl

[24] K.L. Stellmacher, Ein Beispel einer Huygensschen Differentialgleichung, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl., II, 10, 1953, p. 133. | MR | Zbl

[25] K.L. Stellmacher, Eine Klasse von Huygensschen Differentialgleichungen und ihre Integration, Math. Ann., 130, 1955, p. 219. | MR | Zbl

[26] V. Wünsch, Über selbstadjungiete Huygenssche Differentialglechungen mit vier unabhängen Variablen, Math. Nach., 47, 1970, p. 131. | MR | Zbl

[27] V. Wünsch, Maxwellsche Gleichungen und Huygensches Prinzip II. Math. Nach., 73, 1976, p. 19. | MR | Zbl

[28] V. Wünsch, Cauchy-Problem und Huygenssches Prinzip bei einigen-Klassen spinorieller Feldgleichungen II, Beitr. zur Analysis, 13, 1979, p. 147. | MR | Zbl

[29] V. Wünsch, Huygens' Principle on Petrov Type D Space-times, Ann. Physik., 46, 1989, p. 593. | MR | Zbl