Short waves through thin interfaces and 2-microlocal measures
Journées équations aux dérivées partielles (1997), article no. 12, 12 p. 
@article{JEDP_1997____A12_0,
     author = {Miller, Luc},
     title = {Short waves through thin interfaces and 2-microlocal measures},
     journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
     eid = {12},
     pages = {1--12},
     publisher = {Ecole polytechnique},
     year = {1997},
     zbl = {01808670},
     language = {en},
     url = {http://www.numdam.org/item/JEDP_1997____A12_0/}
}
TY  - JOUR
AU  - Miller, Luc
TI  - Short waves through thin interfaces and 2-microlocal measures
JO  - Journées équations aux dérivées partielles
PY  - 1997
SP  - 1
EP  - 12
PB  - Ecole polytechnique
UR  - http://www.numdam.org/item/JEDP_1997____A12_0/
LA  - en
ID  - JEDP_1997____A12_0
ER  - 
%0 Journal Article
%A Miller, Luc
%T Short waves through thin interfaces and 2-microlocal measures
%J Journées équations aux dérivées partielles
%D 1997
%P 1-12
%I Ecole polytechnique
%U http://www.numdam.org/item/JEDP_1997____A12_0/
%G en
%F JEDP_1997____A12_0
Miller, Luc. Short waves through thin interfaces and 2-microlocal measures. Journées équations aux dérivées partielles (1997), article  no. 12, 12 p. http://www.numdam.org/item/JEDP_1997____A12_0/

[1] J.-M. Bony and N. Lerner. Quantification asymptotique et microlocalisation d'ordre supérieur. Ann Scient. Ec Norm Sup., 22:377-433, 1989. | Numdam | MR | Zbl

[2] N. Burq. Mesures semi-classiques et mesures de défaut. Séminaire Bourbaki n° 826, 1997. To appear in Astérisque. | Numdam | MR | Zbl

[3] C. Fermanian-Kammerer. Equation de la Chaleur et Mesures semi-classiques. PhD thesis, Université de Paris-Sud, U.F.R. Scientifique d'Orsay, 1995.

[4] G.A. Francfort and F. Murat. Oscillations and energy densities in the wave equation. Comm. in P.D.E., 17:1785-1865, 1992. | MR | Zbl

[5] P. Gérard. Mesures semi-classiques et ondes de Bloch. In Sém. E.D.P. 1990-1991, exp. XVI. Centre de Mathématiques de l'Ecole Polytechnique, 1991. | Numdam | MR | Zbl

[6] P. Gérard. Microlocal defect measures. Comm. Partial Diff. Eq., 16:1761-1794, 1991. | MR | Zbl

[7] P. Gérard. Oscillations and concentration effects in semilinear wave equations. J. of Funct. Analysis, 141(1):60-98, 1996. | MR | Zbl

[8] P. Gérard and E. Leichtnam. Ergodic properties of eigenfunctions for the Dirichlet problem. Duke Math. J., 71:559-607, 1993. | MR | Zbl

[9] P. Gérard, A. Markowich, N.J. Mauser, and F. Poupaud. Homogenization limits and Wigner transforms. Comm. Pure Appl. Math., L:0321-0377, 1997. | Zbl

[10] F. Gesztesy, R. Nowell, and W. Pötz. One-dimensional scattering theory for quantum systems with nontrivial spatial asymptotics. Technical report, 1995. | Zbl

[11] G. A. Hagedorn and W. R. E. Weiss. Reflection and transmission of high frequency pulses at an interface. Transport Theory and Stat. Phys., 14(5):539-565, 1985. | MR | Zbl

[12] L. Hörmander. The Analysis of Linear Partial Differential Operators. Springer, t. I, 1983, t. III, 1985. | Zbl

[13] P.-L. Lions and T. Paul. Sur les mesures de Wigner. Rev. Mat. Iberoamericana, 9:553-618, 1993. | MR | Zbl

[14] R.B. Melrose and J. Sjöstrand. Singularities of boundary value problems. I. Comm. Pure Appl. Math., 31:593-617, 1978. | MR | Zbl

[15] L. Miller. Réfraction d'ondes semi-classiques par des interfaces franches. To appear in C. R. Acad. Sci. Paris. | Zbl

[16] L. Miller. Propagation d'ondes semi-classiques à travers une interface et mesures 2-microlocales. Doctorat de l'École Polytechnique, Palaiseau, 1996.

[17] F. Nier. A semi-classical picture of quantum scattering. Ann scient. Ec. Norm. Sup., 4e Série, 29(2):149-183, 1996. | Numdam | MR | Zbl

[18] S. N. M. Ruijsenaars and P. J. M. Bongaarts. Scattering theory for one-dimensional step-potentials. Ann. Inst. H. Poincaré, 26:1-17, 1977. | Numdam | MR | Zbl

[19] L.V. Ryzhik, J.B. Keller, and G.C. Papanicolaou. Transport equations for waves in a half space. Technical report, Stanford U., 1996.

[20] A.I. Shnirelman. On the asymptotic properties of eigenfunctions in the regions of chaotic motion. In V. F. Lazutkin, editor, The KAM Theory and Asymptotics of Spectrum of Elliptic Operators, addendum, pages 312-337. Springer, 1991.

[21] L. Tartar. H-measures, a new approach for studying homogenization, oscillations and concentration effects in partial differential equations. Proc. Roy. Soc. Edinburgh, 115(A):193-230, 1990. | MR | Zbl

[22] M. Taylor. Grazing rays and reflection of singularities of solutions to wave equations Part II (Systems). Comm. Pure Appl. Math., 29:463-481, 1976. | MR | Zbl