Propagation des singularités pour des problèmes aux limites
Séminaire Bourbaki : vol. 1978/79, exposés 525-542, Séminaire Bourbaki, no. 21 (1980), Exposé no. 525, 20 p.
@incollection{SB_1978-1979__21__1_0,
     author = {Helffer, Bernard},
     title = {Propagation des singularit\'es pour des probl\`emes aux limites},
     booktitle = {S\'eminaire Bourbaki : vol. 1978/79, expos\'es 525-542},
     series = {S\'eminaire Bourbaki},
     note = {talk:525},
     pages = {1--20},
     publisher = {Springer-Verlag},
     number = {21},
     year = {1980},
     mrnumber = {572414},
     zbl = {0426.35100},
     language = {fr},
     url = {http://archive.numdam.org/item/SB_1978-1979__21__1_0/}
}
TY  - CHAP
AU  - Helffer, Bernard
TI  - Propagation des singularités pour des problèmes aux limites
BT  - Séminaire Bourbaki : vol. 1978/79, exposés 525-542
AU  - Collectif
T3  - Séminaire Bourbaki
N1  - talk:525
PY  - 1980
SP  - 1
EP  - 20
IS  - 21
PB  - Springer-Verlag
UR  - http://archive.numdam.org/item/SB_1978-1979__21__1_0/
LA  - fr
ID  - SB_1978-1979__21__1_0
ER  - 
%0 Book Section
%A Helffer, Bernard
%T Propagation des singularités pour des problèmes aux limites
%B Séminaire Bourbaki : vol. 1978/79, exposés 525-542
%A Collectif
%S Séminaire Bourbaki
%Z talk:525
%D 1980
%P 1-20
%N 21
%I Springer-Verlag
%U http://archive.numdam.org/item/SB_1978-1979__21__1_0/
%G fr
%F SB_1978-1979__21__1_0
Helffer, Bernard. Propagation des singularités pour des problèmes aux limites, dans Séminaire Bourbaki : vol. 1978/79, exposés 525-542, Séminaire Bourbaki, no. 21 (1980), Exposé no. 525, 20 p. http://archive.numdam.org/item/SB_1978-1979__21__1_0/

[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. | MR | Zbl

[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. | Numdam | MR | Zbl

[3] L. Boutet De Monvel - Boundary problems for pseudo-differential operators, Acta Math., 126 (1971), p. 11-51. | MR | Zbl

[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. | MR | Zbl

[5] J. Chazarain - Le problème mixte, Séminaire Bourbaki, Exposé 432, juin 1973, Lecture Notes in Math. n° 383, p. 265-285, Springer-Verlag, 1974. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

[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. | Numdam | MR | Zbl

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

[9] J.J. Duistermaat - Fourier Intégral operators, Courant Institute Lecture Notes, New York, (1973). | MR | Zbl

[10] J.J. Duistermaat - Oscillatory integrals, Lagrange immersions and Unfolding of singularities, Comm. Pure Appl. Math., 27 (1974), p. 135-142. | MR | Zbl

[11] J.J. Duistermaat and L. Hormander - Fourier integral operators II, Acta Math., 128 (1972), p. 183-259. | MR | Zbl

[12] G. Eskin - A parametrix for mixed problems for strictly hyperbolic of arbitrary order, Comm. in p. d. e., vol. 1, n° 6 (1976). | MR | Zbl

[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. | Numdam | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[16] Guillemin - R.B. Melrose - The Poisson summation formula for manifolds with boundary, Preprint.

[17] L. Hormander - Linear partial differential équations, Springer-Verlag, Berlin, 1963.

[18] L. Hörmander - Pseudodifferential operators and non-elliptic boundary value problems, Ann. of Math., 83 (1966), p. 129-209. | MR | Zbl

[19] L. Hörmander - Linear Differential Operators, Actes du Congrès International, 1970, tome 1, p. 121-133. | MR | Zbl

[20] L. Hörmander - Fourier intégral operators I, Acta Math., 127 (1971), p. 79- 183. | MR | Zbl

[21] L. Hörmander - On the existence and regularity of solutions of linear pseudodifferential equations, Enseignement Math., 17 (1971), p. 99-163. | MR | Zbl

[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. | Zbl

[23] P.D. Lax and R. Philipps - Scattering theory, Acad. Press New York, 1967. | MR | Zbl

[24] D. Ludwig - Uniform asymptotic expansions at a caustic, Comm. Pure Appl. Math., vol. 19 (1966), p. 215-250. | MR | Zbl

[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. | MR | Zbl

[26] A. Majda and S. Osher - Reflection of singularities at the boundary, Comm. Pure Appl. Math., vol. 28 (1975), p. 479-499. | MR | Zbl

[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. | MR | Zbl

[28] R.B. Melrose - Local Fourier - Airy intégral operators, Duke Math. Journal, vol. 42, n° 4, (1975), p. 583-604. | MR | Zbl

[29] R.B. Melrose - Microlocal parametrices for diffractive boundary value problems, Duke Math. Journal, vol. 42 (1975), p. 605-635. | MR | Zbl

[30] R.B. Melrose - Equivalence of glancing hypersurfaces (I) and (II), Inventiones Math., 37 (1976), p. 165-191, et à paraître. | MR | Zbl

[31] R.B. Melrose - Airy Operators, Comm. in P. D. E., 3(1) (1978), p. 1-76. | MR | Zbl

[32] R.B. Melrose - Differential boundary value problems of principal type, Séminaire à Princeton (1977). | Zbl

[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). | MR | Zbl

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

[35] R.B. Melrose - Singularities and energy decay in acoustical scattering, à paraître. | Zbl

[36] R.B. Melrose - Transformation of boundary problems, en préparation. | Zbl

[37] C. Morawetz and D. Ludwig - The generalized Huygens' principle for reflecting bodies, Comm. Pure Appl. Math., 22 (1969), p. 189-205. | MR | Zbl

[38] Morawetz - Ralston - Strauss - Decay of solutions of the wave equation outside non-trapping obstacles, Comm. Pure Appl. Math., 30 (1977), p. 447-508. | MR | Zbl

[39] L. Nirenberg - Lectures on linear partial differential equations, CBMS Regional Conf. Ser. in Math., n° 17, Amer. Math. Soc., Providence R.I., (1973). | MR | Zbl

[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. | MR | Zbl

[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. | Zbl

[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° 6 Ecole Polytechnique. Séminaire Goulaouic-Schwartz, 1976/77, Exposé n° 9 | Numdam | MR | Zbl

[43] M.E. Taylor - Reflection of singulafities of solutions to systems of differential equations, Comm. Pure Appl. Math., 28 (1975), p. 457-478. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | Zbl