[Diffraction par singularités conormales]
Dans cet article nous montrons que, pour une métrique avec des singularités conormales qui correspondent à la classe , , l'onde réfléchie est plus régulière que l'onde incidente dans un sens Sobolev. Cela s'avère utile à l'analyse des séries de diffusion multiple, les termes d'ordres les plus élevés pouvant être ôtés de manière effective.
In this paper we show that for metrics with conormal singularities that correspond to class , , the reflected wave is more regular than the incident wave in a Sobolev sense. This is helpful in the analysis of the multiple scattering series since higher order terms can be effectively `peeled off'.
DOI : 10.24033/asens.2247
Keywords: Wave equation, conormal singularities, diffraction, reflection, paired Lagrangian distributions.
Mot clés : Équation d'onde, singularités conormales, diffraction, réflexion, distributions aux intersections lagrangiennes.
@article{ASENS_2015__48_2_351_0,
author = {de Hoop, Maarten and Uhlmann, Gunther and Vasy, Andr\'as},
title = {Diffraction from conormal singularities},
journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
pages = {351--408},
publisher = {Soci\'et\'e Math\'ematique de France. Tous droits r\'eserv\'es},
volume = {Ser. 4, 48},
number = {2},
year = {2015},
doi = {10.24033/asens.2247},
zbl = {1322.58025},
language = {en},
url = {http://www.numdam.org/articles/10.24033/asens.2247/}
}
TY - JOUR AU - de Hoop, Maarten AU - Uhlmann, Gunther AU - Vasy, András TI - Diffraction from conormal singularities JO - Annales scientifiques de l'École Normale Supérieure PY - 2015 SP - 351 EP - 408 VL - 48 IS - 2 PB - Société Mathématique de France. Tous droits réservés UR - http://www.numdam.org/articles/10.24033/asens.2247/ DO - 10.24033/asens.2247 LA - en ID - ASENS_2015__48_2_351_0 ER -
%0 Journal Article %A de Hoop, Maarten %A Uhlmann, Gunther %A Vasy, András %T Diffraction from conormal singularities %J Annales scientifiques de l'École Normale Supérieure %D 2015 %P 351-408 %V 48 %N 2 %I Société Mathématique de France. Tous droits réservés %U http://www.numdam.org/articles/10.24033/asens.2247/ %R 10.24033/asens.2247 %G en %F ASENS_2015__48_2_351_0
de Hoop, Maarten; Uhlmann, Gunther; Vasy, András. Diffraction from conormal singularities. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 48 (2015) no. 2, pp. 351-408. doi : 10.24033/asens.2247. http://www.numdam.org/articles/10.24033/asens.2247/
, Pseudodifferential operators and applications (Notre Dame, Ind., 1984) (Proc. Sympos. Pure Math.), Volume 43, Amer. Math. Soc., Providence, RI, 1985, pp. 5-16 | DOI | MR | Zbl
A phase space transform adapted to the wave equation, Comm. Partial Differential Equations, Volume 32 (2007), pp. 1065-1101 (ISSN: 0360-5302) | DOI | MR | Zbl
Characteristic space-time estimates for the wave equation, Math. Z., Volume 236 (2001), pp. 113-131 (ISSN: 0025-5874) | DOI | MR | Zbl
Oscillatory integrals with singular symbols, Duke Math. J., Volume 48 (1981), pp. 251-267 http://projecteuclid.org/euclid.dmj/1077314493 (ISSN: 0012-7094) | DOI | MR | Zbl
Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, J. Funct. Anal., Volume 89 (1990), pp. 202-232 (ISSN: 0022-1236) | DOI | MR | Zbl
Recovering singularities of a potential from singularities of scattering data, Comm. Math. Phys., Volume 157 (1993), pp. 549-572 http://projecteuclid.org/euclid.cmp/1104254021 (ISSN: 0010-3616) | DOI | MR | Zbl
Fourier integral operators. I, Acta Math., Volume 127 (1971), pp. 79-183 (ISSN: 0001-5962) | DOI | MR | Zbl
On the existence and the regularity of solutions of linear pseudo-differential equations, Enseignement Math., Volume 17 (1971), pp. 99-163 (ISSN: 0013-8584) | MR | Zbl
, Springer, 1983 (4 vols.)
Propagation des ondes dans les variétés à coins, Ann. Sci. École Norm. Sup., Volume 30 (1997), pp. 429-497 (ISSN: 0012-9593) | DOI | Numdam | MR | Zbl
Transformation of boundary problems, Acta Math., Volume 147 (1981), pp. 149-236 (ISSN: 0001-5962) | DOI | MR | Zbl
, Research Notes in Math., 4, A K Peters, Ltd., Wellesley, MA, 1993, 377 pages (ISBN: 1-56881-002-4) | MR | Zbl
Analytic -theory on manifolds with corners, Adv. Math., Volume 92 (1992), pp. 1-26 (ISSN: 0001-8708) | DOI | MR | Zbl
Singularities of boundary value problems. I, Comm. Pure Appl. Math., Volume 31 (1978), pp. 593-617 (ISSN: 0010-3640) | DOI | MR | Zbl
Singularities of boundary value problems. II, Comm. Pure Appl. Math., Volume 35 (1982), pp. 129-168 (ISSN: 0010-3640) | DOI | MR | Zbl
Lagrangian intersection and the Cauchy problem, Comm. Pure Appl. Math., Volume 32 (1979), pp. 483-519 (ISSN: 0010-3640) | DOI | MR | Zbl
A parametrix construction for wave equations with coefficients, Ann. Inst. Fourier (Grenoble), Volume 48 (1998), pp. 797-835 (ISSN: 0373-0956) | DOI | Numdam | MR | Zbl
On the norm of spectral clusters for compact manifolds with boundary, Acta Math., Volume 198 (2007), pp. 107-153 (ISSN: 0001-5962) | DOI | MR | Zbl
Strichartz estimates for operators with nonsmooth coefficients and the nonlinear wave equation, Amer. J. Math., Volume 122 (2000), pp. 349-376 http://muse.jhu.edu/journals/american_journal_of_mathematics/v122/122.2tataru.pdf (ISSN: 0002-9327) | DOI | MR | Zbl
Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients. III, J. Amer. Math. Soc., Volume 15 (2002), pp. 419-442 (ISSN: 0894-0347) | DOI | MR | Zbl
, Mathematical Surveys and Monographs, 81, Amer. Math. Soc., Providence, RI, 2000, 257 pages (ISBN: 0-8218-2633-6) | MR | Zbl
, Recent advances in differential equations and mathematical physics (Contemp. Math.), Volume 412, Amer. Math. Soc., Providence, RI, 2006, pp. 315-333 | DOI | MR | Zbl
Propagation of singularities for the wave equation on manifolds with corners, Ann. of Math., Volume 168 (2008), pp. 749-812 (ISSN: 0003-486X) | DOI | MR | Zbl
Diffraction at corners for the wave equation on differential forms, Comm. Partial Differential Equations, Volume 35 (2010), pp. 1236-1275 (ISSN: 0360-5302) | DOI | MR | Zbl
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