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Régularité lipschitzienne et solutions de l’équation des ondes sur une variété riemannienne compacte. (French) Zbl 0359.35042


MSC:

35L05 Wave equation
35D10 Regularity of generalized solutions of PDE (MSC2000)
35S99 Pseudodifferential operators and other generalizations of partial differential operators
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
58J40 Pseudodifferential and Fourier integral operators on manifolds
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References:

[1] V. I. ARNOLD , On a Caracteristic Class Entering in the Quantizations Conditions (Funct. Anal. and its Appl., Vol. 1, 1967 , p. 1-13). Zbl 0175.20303 · Zbl 0175.20303
[2] V. I. ARNOLD , Integrals of Rapidly Oscillating Functions and Singularities of Projections of Lagrangien Manifolds (Funct. Anal. and its Appl., vol. 6, n^\circ 3, 1972 , p. 61-62). MR 50 #8594 | Zbl 0278.57010 · Zbl 0278.57010 · doi:10.1007/BF01077879
[3] M. BERGER , Communication orale.
[4] A. BESSE , Manifolds all of Whose Geodesics are Closed (Ergebmisse der Math. und Grenzgebiete). Springer-Verlag (à paraître). Zbl 0387.53010 · Zbl 0387.53010
[5] J.-L. CLERC et P. COURRÈGE , Une algèbre d’opérateurs intégraux singuliers dans les espaces C\mu pour 0 < \mu < 1 (C. R. Acad. Sc. Paris, t. 269, série A, 1968 , p. 967-969). MR 42 #6654 | Zbl 0186.47102 · Zbl 0186.47102
[6] Y. COLIN DE VERDIÈRE et M. FRISCH , Régularité lipschitzienne et solutions de l’équation des ondes sur une variété riemannienne compacte (C. R. Acad. Sc. Paris, t. 282, série A, 1976 , p. 783-786). MR 53 #9295 | Zbl 0324.35010 · Zbl 0324.35010
[7] A. P. CALDERON and A. ZYGMUND , On the existence of Certain Singular Integrals (Acta Math., vol. 88, 1952 , p. 85-139). MR 14,637f | Zbl 0047.10201 · Zbl 0047.10201 · doi:10.1007/BF02392130
[8] J. J. DUISTERMAAT , Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities (Comm. on Pure and Applied Math., vol. 27, 1974 , p. 207-281). MR 53 #9306 | Zbl 0285.35010 · Zbl 0285.35010 · doi:10.1002/cpa.3160270205
[9] J. J. DUISTERMAAT and V. GUILLEMIN , The Spectrum of Positiv Elliptic Operators and Periodic Geodesics (Invent. Math., vol. 29, 1975 , p. 39-79). MR 53 #9307 | Zbl 0307.35071 · Zbl 0307.35071 · doi:10.1007/BF01405172
[10] J. J. DUISTERMAAT and L. HÖRMANDER , Fourier Integral Operators, II (Acta Math., vol. 128, 1972 , p. 183-269). MR 52 #9300 | Zbl 0232.47055 · Zbl 0232.47055 · doi:10.1007/BF02392165
[11] M. FRISCH , Propriétés asymptotiques des vibrations du tore (J. Math. pures et appl., vol. 54, 1975 , p. 285-304). MR 56 #1374 | Zbl 0286.35012 · Zbl 0286.35012
[12] M. FRISCH , Propriétés asymptotiques des vibrations des sphères (J. Math. pures et appl.) vol. 55, 1976 , p. 421-430. MR 56 #9603 | Zbl 0343.35049 · Zbl 0343.35049
[13] M. GOLUBITSKY and V. GUILLEMIN , Stable Mappings and their Singularities (Graduate Texts in Math., vol. 14, 1973 , Springer-Verlag). MR 49 #6269 | Zbl 0294.58004 · Zbl 0294.58004
[14] V. GUILLEMIN and D. SCHAEFFER , Remarks on a Paper of D.Ludwig (Bull. Amer. Math. Soc., vol. 79, n^\circ 2, 1973 , p. 382-385). Article | MR 53 #13800 | Zbl 0256.35008 · Zbl 0256.35008 · doi:10.1090/S0002-9904-1973-13176-3
[15] I. M. GUELFAND et G. E. CHILOV , Les distributions , t. 1, Dunod, Paris, 1962 . MR 24 #A2235 | Zbl 0115.10102 · Zbl 0115.10102
[16] L. HÖRMANDER , Fourier Integral Operators I (Acta Math., vol. 127, 1971 , p. 79-183). MR 52 #9299 | Zbl 0212.46601 · Zbl 0212.46601 · doi:10.1007/BF02392052
[17] L. HÖRMANDER , The Spectral Function of an Elliptic Operator (Acta Math., vol. 121, 1968 , p. 193-218). MR 58 #29418 | Zbl 0164.13201 · Zbl 0164.13201 · doi:10.1007/BF02391913
[18] S. HELGASON , Differential Geometry and Symmetric Spaces , Academic Press, New York, 1962 . MR 26 #2986 | Zbl 0111.18101 · Zbl 0111.18101
[19] Y. MEYER , Trois problèmes sur les sommes trigonométriques . 1 : propriétés asymptotiques des vibrations des sphères (Astérisque, vol. 1, S.M.F., 1973 ). MR 57 #3096 | Zbl 0318.42002 · Zbl 0318.42002
[20] Y. MEYER , Théorie Lp des sommes trigonométriques apériodiques (Ann. Inst. Fourier, Grenoble, vol. 24, n^\circ 4, 1974 , p. 189-211). Numdam | MR 51 #8716 | Zbl 0287.42003 · Zbl 0287.42003 · doi:10.5802/aif.538
[21] L. NIRENBERG , Lectures on Linear Partial Differential Equations (Reg. Conf. series in Math., n^\circ 20, Amer. Math. Soc., 1973 ). MR 56 #9048 · Zbl 0267.35001
[22] E. M. STEIN , Singular Integrals and Differentiability Properties of Functions , Princeton University Press, 1970 . MR 44 #7280 | Zbl 0207.13501 · Zbl 0207.13501
[23] E. M. STEIN and G. WEISS , Introduction to Fourier Analysis on Euclidean Spaces , Princeton University Press, 1971 . MR 46 #4102 | Zbl 0232.42007 · Zbl 0232.42007
[24] E. M. STEIN and A. ZYGMUND , Boundedness of Translation Invariant Operators in Hölder Spaces and Lp Spaces (Ann. of Math., vol. 85, 1967 , p. 337-349). MR 35 #5964 | Zbl 0172.40102 · Zbl 0172.40102 · doi:10.2307/1970445
[25] A. WEINSTEIN , The Generic Conjugate Locus [Proc. Symp. in Pure Math. (A.M.S.), vol. 15, 1968 ]. Zbl 0205.25803 · Zbl 0205.25803
[26] W. WASOW , Asymptotic Expansions for Ordinary Differential Equations (Interscience, New York, 1965 ). MR 34 #3041 | Zbl 0133.35301 · Zbl 0133.35301
[27] F. W. WARNER , The Conjugate Locus of a Riemannian Manifold (Amer. J. Math., vol. 87, 1965 , p. 575-604). MR 34 #8344 | Zbl 0129.36002 · Zbl 0129.36002 · doi:10.2307/2373064
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