Propagation des singularités pour des problèmes aux limites

 Access to full text

 Full (PDF)

1. [1] K.G. Andersson - Analytic wave front sets for solutions of linear differential équations of principal type, Trans. Amer. Math. Soc., 177(1973), p. 1-27. Zbl0259.35072MR316871
2. [2] K.G. Andersson and R.B. Melrose - The propagation of singularities along gliding Rays, Inventiones Math., 41 (1977), p. 197-232 ; et exposé n° 1, Séminaire Goulaouic-Schwartz, 1976/77, Ecole Polytechnique. Zbl0373.35053MR494322
3. [3] L. Boutet De Monvel - Boundary problems for pseudo-differential operators, Acta Math., 126 (1971), p. 11-51. Zbl0206.39401MR407904
4. [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. Zbl0253.35058MR320536
5. [5] J. Chazarain - Le problème mixte, Séminaire Bourbaki, Exposé 432, juin 1973, Lecture Notes in Math. n° 383, p. 265-285, Springer-Verlag, 1974. Zbl0289.35057MR440208
6. [6] J. Chazarain - Spectre des opérateurs elliptiques et flots hamiltoniens, Séminaire Bourbaki, Exposé 460, Février 1975, Lecture Notes in Math. n° 514, p. 111-123, Springer-Verlag, 1976. Zbl0338.58017MR445564
7. [7] J. Chazarain - Paramétrixe du problème mixte pour l'équation des ondes à l'intérieur d'un domaine convexe pour les bicaractéristiques, Astérisque n° 34/35, (1976), p. 165-182. Zbl0329.35039MR509765
8. [8] J. Chazarain - Reflection of singularities for a class of operators with multiple characteristics, Publ. R. I. M. S. Kyoto Univ., (1976). 
9. [9] J.J. Duistermaat - Fourier Intégral operators, Courant Institute Lecture Notes, New York, (1973). Zbl0272.47028MR451313
10. [10] J.J. Duistermaat - Oscillatory integrals, Lagrange immersions and Unfolding of singularities, Comm. Pure Appl. Math., 27 (1974), p. 135-142. Zbl0285.35010MR405513
11. [11] J.J. Duistermaat and L. Hormander - Fourier integral operators II, Acta Math., 128 (1972), p. 183-259. Zbl0232.47055MR388464
12. [12] G. Eskin - A parametrix for mixed problems for strictly hyperbolic of arbitrary order, Comm. in p. d. e., vol. 1, n° 6 (1976). Zbl0355.35053MR509777
13. [13] G. Eskin - A parametrix for interior mixed problems for strictly hyperbolic équations, Journal d'Analyse Mathématique de Jérusalem, vol. 32 (1977), p. 17-61, ou Séminaire Goulaouic-Schwartz, 1976/77, exposé 12, Ecole Polytechnique. Zbl0375.35037
14. [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. Zbl0319.35053MR393861
15. [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. Zbl0356.35056MR437938
16. [16] Guillemin - R.B. Melrose - The Poisson summation formula for manifolds with boundary, Preprint. 
17. [17] L. Hormander - Linear partial differential équations, Springer-Verlag, Berlin, 1963. 
18. [18] L. Hörmander - Pseudodifferential operators and non-elliptic boundary value problems, Ann. of Math., 83 (1966), p. 129-209. Zbl0132.07402MR233064
19. [19] L. Hörmander - Linear Differential Operators, Actes du Congrès International, 1970, tome 1, p. 121-133. Zbl0223.35083MR513000
20. [20] L. Hörmander - Fourier intégral operators I, Acta Math., 127 (1971), p. 79- 183. Zbl0212.46601MR388463
21. [21] L. Hörmander - On the existence and regularity of solutions of linear pseudodifferential equations, Enseignement Math., 17 (1971), p. 99-163. Zbl0224.35084MR331124
22. [22] Ja.V. Ivrii - Non classical distribution of singularities of the wave equation solution near the boundary, Doklady Acad. Nauk CCCP, tome 241 (1978), n° 5, p. 1013-1016. Zbl0413.35042
23. [23] P.D. Lax and R. Philipps - Scattering theory, Acad. PressNew York, 1967. Zbl0186.16301MR217440
24. [24] D. Ludwig - Uniform asymptotic expansions at a caustic, Comm. Pure Appl. Math., vol. 19 (1966), p. 215-250. Zbl0163.13703MR196254
25. [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. Zbl0154.12802MR204032
26. [26] A. Majda and S. Osher - Reflection of singularities at the boundary, Comm. Pure Appl. Math., vol. 28 (1975), p. 479-499. Zbl0307.35077MR492792
27. [27] A. Melin and J. Sjöstrand - A calculus for F. I. O. in domains with boundary and applications to the oblique dérivative problem, Comm, in P. D. E., 2 (1977), p. 857-935. Zbl0392.35055MR458508
28. [28] R.B. Melrose - Local Fourier - Airy intégral operators, Duke Math. Journal, vol. 42, n° 4, (1975), p. 583-604. Zbl0368.35054MR517100
29. [29] R.B. Melrose - Microlocal parametrices for diffractive boundary value problems, Duke Math. Journal, vol. 42 (1975), p. 605-635. Zbl0368.35055MR517101
30. [30] R.B. Melrose - Equivalence of glancing hypersurfaces (I) and (II), Inventiones Math., 37 (1976), p. 165-191, et à paraître. Zbl0354.53033MR436225
31. [31] R.B. Melrose - Airy Operators, Comm. in P. D. E., 3(1) (1978), p. 1-76. Zbl0384.35052MR493116
32. [32] R.B. Melrose - Differential boundary value problems of principal type, Séminaire à Princeton (1977). Zbl0447.35053
33. [33] R.B. Melrose and J. Sjöstrand - Singularities of boundary value problems, I and II : Comm. Pure Appl. Math., vol. XXXI, n° 5, (1978), p. 593-619 ; et en préparation (et Sém. Goulaouic-Schwartz, 77-78, Exposé n° 15). Zbl0368.35020MR492794
34. [34] R.B. Melrose - Singularities of solutions to boundary value problems, Actes du Congrès International des Math. d'Helsinki (1978). Zbl0452.35120
35. [35] R.B. Melrose - Singularities and energy decay in acoustical scattering, à paraître. Zbl0415.35050
36. [36] R.B. Melrose - Transformation of boundary problems, en préparation. Zbl0492.58023
37. [37] C. Morawetz and D. Ludwig - The generalized Huygens' principle for reflecting bodies, Comm. Pure Appl. Math., 22 (1969), p. 189-205. Zbl0167.10102MR605677
38. [38] Morawetz - Ralston - Strauss - Decay of solutions of the wave equation outside non-trapping obstacles, Comm. Pure Appl. Math., 30 (1977), p. 447-508. Zbl0372.35008MR509770
39. [39] L. Nirenberg - Lectures on linear partial differential equations, CBMS Regional Conf. Ser. in Math., n° 17, Amer. Math. Soc., Providence R.I., (1973). Zbl0267.35001MR450755
40. [40] T. Oshima - On Analytic Equivalence of Glancing Hypersurfaces, Sci. Papers of the Coll. of General Education, University of Tokyo, vol. 28, n° 1 (1978), p. 51-57. Zbl0382.53026MR494335
41. [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. Zbl0156.11501
42. [42] P. Schapira - Propagation au bord et réflexion des singularités analytiques des solutions des équations aux dérivées partielles, Séminaire Goulaouic-Schwartz, 1975/76, Exposé n° 6Ecole Polytechnique. Séminaire Goulaouic-Schwartz, 1976/77, Exposé n° 9 Zbl0338.35085MR467853
43. [43] M.E. Taylor - Reflection of singulafities of solutions to systems of differential equations, Comm. Pure Appl. Math., 28 (1975), p. 457-478. Zbl0332.35058MR509098
44. [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. Zbl0335.35059MR397175
45. [45] M.E. Taylor - Propagation, reflection, and diffraction of singularities of solutions to wave equations, Bull. Amer. Math. Soc., vol. 84, n° 4, Juillet 1978. Zbl0385.35036MR489757
46. [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. Zbl0432.73021