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Propagation des singularités pour des problèmes aux limites [d'après R. B. Melrose, J. Sjöstrand]

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Séminaire Bourbaki vol. 1978/79 Exposés 525 – 542

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 770))

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Bibliographie

  1. K. G. ANDERSSON-Analytic wave front sets for solutions of linear differential equations of principal type, Trans. Amer. Math. Soc., 177(1973), p. 1–27.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. G. ANDERSSON and R. B. MELROSE-The propagation of singularities along gliding Rays, Inventiones Math., 41 (1977), p. 197–232; et exposé no 1, Séminaire Goulaouic-Schwartz, 1976/77, Ecole Polytechnique.

    Article  MATH  MathSciNet  Google Scholar 

  3. L. BOUTET DE MONVEL-Boundary problems for pseudo-differential operators, Acta Math., 126 (1971), p. 11–51.

    Article  MATH  MathSciNet  Google Scholar 

  4. J. CHAZARAIN-Construction de la paramétrixe du problème mixte pour l'équation des ondes, C. R. Acad. Sci. Paris, t. 276 (1973), p. 1212–1215.

    MathSciNet  Google Scholar 

  5. J. CHAZARAIN-Le problème mixte, Séminaire Bourbaki, Exposé 432, juin 1973, Lecture Notes in Math. no 383, p. 265–285, Springer-Verlag, 1974.

    Google Scholar 

  6. J. CHAZARAIN-Spectre des opérateurs elliptiques et flots hamiltoniens, Séminaire Bourbaki, Exposé 460, Février 1975, Lecture Notes in Math. no 514, p. 111–123, Springer-Verlag, 1976.

    Google Scholar 

  7. J. CHAZARAIN-Paramétrixe du problème mixte pour l'équation des ondes à l'intérieur d'un domaine convexe pour les bicaractéristiques, Astérisque no 34/35, (1976), p. 165–182.

    Google Scholar 

  8. J. CHAZARAIN-Reflection of singularities for a class of operators with multiple characteristics, Publ. R. I. M. S. Kyoto Univ., (1976).

    Google Scholar 

  9. J. J. DUISTERMAAT-Fourier Integral operators, Courant Institute Lecture Notes, New York, (1973).

    Google Scholar 

  10. J. J. DUISTERMAAT-Oscillatory integrals, Lagrange immersions and Unfolding of singularities, Comm. Pure Appl. Math., 27 (1974), p. 135–142.

    MathSciNet  Google Scholar 

  11. J. J. DUISTERMAAT and L. HÖRMANDER-Fourier integral operators II, Acta Math., 128 (1972), p. 183–259.

    Article  MATH  MathSciNet  Google Scholar 

  12. G. ESKIN-A parametrix for mixed problems for strictly hyperbolic of arbitrary order, Comm. in p. d. e., vol. 1, no 6 (1976).

    Google Scholar 

  13. G. ESKIN-A parametrix for interior mixed problems for strictly hyperbolic equations, Journal d'Analyse Mathématique de Jérusalem, vol. 32 (1977), p. 17–61, ou Séminaire Goulaouic-Schwartz, 1976/77, exposé 12, Ecole Polytechnique.

    Google Scholar 

  14. F. G. FRIEDLANDER-The Wave front set of the solution of a simple initial boundary value problem with glancing rays, Proc. Cambridge Philo. Soc., 79(1976), p. 145–159.

    Article  MATH  MathSciNet  Google Scholar 

  15. F. G. FRIEDLANDER and R. B. MELROSE-The wave front set of the solution of a simple initial boundary value problem with glancing rays II, Proc. Cambridge Philos. Soc., 79 (1977), p. 97–120.

    MathSciNet  Google Scholar 

  16. GUILLEMIN-R. B. MELROSE-The Poisson summation formula for manifolds with boundary, Preprint.

    Google Scholar 

  17. L. HÖRMANDER-Linear partial differential equations, Springer-Verlag, Berlin, 1963.

    MATH  Google Scholar 

  18. L. HÖRMANDER-Pseudodifferential operators and non-elliptic boundary value problems, Ann. of Math., 83 (1966), p. 129–209.

    Article  MATH  MathSciNet  Google Scholar 

  19. L. HÖRMANDER-Linear Differential Operators, Actes du Congrès International, 1970, tome 1, p. 121–133.

    Google Scholar 

  20. L. HÖRMANDER-Fourier integral operators I, Acta Math., 127 (1971), p. 79–183.

    Article  MATH  MathSciNet  Google Scholar 

  21. L. HÖRMANDER-On the existence and regularity of solutions of linear pseudo-differential equations, Enseignement Math., 17 (1971), p. 99–163.

    MATH  MathSciNet  Google Scholar 

  22. Ja. V. IVRII-Non classical distribution of singularities of the wave equation solution near the boundary, Doklady Acad. Nauk CCCP, tome 241 (1978), no 5, p. 1013–1016.

    MATH  MathSciNet  Google Scholar 

  23. P. D. LAX and R. PHILIPPS-Scattering theory, Acad. Press New York, 1967.

    MATH  Google Scholar 

  24. D. LUDWIG-Uniform asymptotic expansions at a caustic, Comm. Pure Appl. Math., vol. 19 (1966), p. 215–250.

    MATH  MathSciNet  Google Scholar 

  25. D. LUDWIG-Uniform asymptotic expansions of the fieldscattered by a convex object at high frequencies, Comm. Pure Appl. Math., vol. 19 (1967), p. 103–138.

    MathSciNet  Google Scholar 

  26. A. MAJDA and S. OSHER-Reflection of singularities at the boundary, Comm. Pure Appl. Math., vol. 28 (1975), p. 479–499.

    MATH  MathSciNet  Google Scholar 

  27. A. MELIN and J. SJÖSTRAND-A calculus for F. I. O. in domains with boundary and applications to the oblique derivative problem, Comm. in P. D. E., 2 (1977), p. 857–935.

    MATH  Google Scholar 

  28. R. B. MELROSE-Local Fourier-Airy integral operators, Duke Math. Journal, vol. 42, no 4, (1975), p. 583–604.

    Article  MATH  MathSciNet  Google Scholar 

  29. R. B. MELROSE-Microlocal parametrices for diffractive boundary value problems, Duke Math. Journal, vol. 42 (1975), p. 605–635.

    Article  MATH  MathSciNet  Google Scholar 

  30. R. B. MELROSE-Equivalence of glancing hypersurfaces (I) and (II), Inventiones Math., 37 (1976), p. 165–191, et à paraître.

    Article  MATH  MathSciNet  Google Scholar 

  31. R. B. MELROSE-Airy Operators, Comm. in P. D. E., 3(1) (1978), p. 1–76.

    MATH  MathSciNet  Google Scholar 

  32. R. B. MELROSE-Differential boundary value problems of principal type, Séminaire à Princeton (1977).

    Google Scholar 

  33. R. B. MELROSE and J. SJÖSTRAND-Singularities of boundary value problems, I and II: Comm. Pure Appl. Math., vol. XXXI, no 5, (1978), p. 593–619; et en préparation (et Sém. Goulaouic-Schwartz, 77–78, Exposé no 15).

    Google Scholar 

  34. R. B. MELROSE-Singularities of solutions to boundary value problems, Actes du Congrès International des Math. d'Helsinki (1978).

    Google Scholar 

  35. R. B. MELROSE-Singularities and energy decay in acoustical scattering, à paraître.

    Google Scholar 

  36. R. B. MELROSE-Transformation of boundary problems, en préparation.

    Google Scholar 

  37. C. MORAWETZ and D. LUDWIG-The generalized Huygens' principle for reflecting bodies, Comm. Pure Appl. Math., 22 (1969), p. 189–205.

    MATH  MathSciNet  Google Scholar 

  38. MORAWETZ-RALSTON-STRAUSS-Decay of solutions of the wave equation outside non-trapping obstacles, Comm. Pure Appl. Math., 30 (1977), p. 447–508.

    MATH  MathSciNet  Google Scholar 

  39. L. NIRENBERG-Lectures on Linear partial differential equations, CBMS Regional Conf. Ser. in Math., no 17, Amer. Math. Soc., Providence R.I., (1973).

    Google Scholar 

  40. T. OSHIMA-On Analytic Equivalence of Glancing Hypersurfaces, Sci. Papers of the Coll. of General Education, University of Tokyo, vol. 28, no 1 (1978), p. 51–57.

    MATH  MathSciNet  Google Scholar 

  41. A. POVZNER and J. SUKHAREVSKII-Discontinuities of the Green's function of a mixed problem for the wave equation, Mat. Sb., 51 (1960), p. 326; Amer. Math. Soc. Transl., (2) 47 (1965), p. 131–156.

    Google Scholar 

  42. P. SCHAPIRA-Propagation au bord et réflexion des singularités analytiques des solutions des équations aux dérivées partielles, Séminaire Goulaouic-Schwartz, 1975/76, Exposé no 6 Séminaire Goulaouic-Schwartz, 1976/77, Exposé no 9 Ecole Polytechnique.

    Google Scholar 

  43. M. E. TAYLOR-Reflection of singularities of solutions to systems of differential equations, Comm. Pure Appl. Math., 28 (1975), p. 457–478.

    MATH  MathSciNet  Google Scholar 

  44. M. E. TAYLOR-Grazing rays and reflection of singularities of solutions to wave equations I, II, III, Comm. Pure Appl. Math., 29 (1976), p. 1–38; p. 463–481; et à paraître.

    MATH  MathSciNet  Google Scholar 

  45. M. E. TAYLOR-Propagation, reflection, and diffraction of singularities of solutions to wave equations, Bull. Amer. Math. Soc., vol. 84, no 4, Juillet 1978.

    Google Scholar 

  46. M. E. TAYLOR-Rayleigh waves in linear elasticity as a propagation of singularities phenomenon: Park City Conf. in P. D. E. and Geometry, (1977), à paraître.

    Google Scholar 

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Helffer, B. (1980). Propagation des singularités pour des problèmes aux limites [d'après R. B. Melrose, J. Sjöstrand]. In: Séminaire Bourbaki vol. 1978/79 Exposés 525 – 542. Lecture Notes in Mathematics, vol 770. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0096232

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  • DOI: https://doi.org/10.1007/BFb0096232

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