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References (16)
-
L. Hörmander (1990)
The analysis of linear partial differential operators -
F. Friedlander, R. Melrose (1977)
The wave front set of the solution of a simple initial-boundary value problem with glancing rays. IIMathematical Proceedings of the Cambridge Philosophical Society, 81
-
P. Laubin, B. Willems (1994)
Distributions associated to a 2-microlocal pair of lagrangian manifoldsComm. in Part. Diff. Ed., 19
-
P. Laubin, B. Willems (1994)
Distributions Associated to a 2-Microlocal Pair of Lagrangian MainfoldsCommunications in Partial Differential Equations, 19
-
G. Lebeau (1986)
Propagation des Singularités Gevrey pour le Problème de Dirichlet -
G. Lebeau (1984)
Regularite gevrey 3 pour la diffractionCommunications in Partial Differential Equations, 9
-
G. Lebeau (1985)
Deuxième microlocalisation sur les sous-variétés isotropesAnn. Inst. Fourier, Grenoble, 35
-
P. Laubin (1997)
Conormality and Lagrangian Properties in Diffractive Boundary Value Problems -
R. Melrose (1981)
Transformation of boundary problemsActa Mathematica, 147
-
G. Lebeau (1982)
Deuxième microlocalisation sur les sous-variétés isotropesAnnales de l'Institut Fourier, 35
-
R. Melrose, G. Uhlmann (1979)
Lagrangian Intersection and the Cauchy ProblemCommunications on Pure and Applied Mathematics, 32
-
C. Bardos, G. Lebeau, J. Rauch (1987)
Scattering frequencies and Gervey 3 singularitiesInventiones mathematicae, 90
-
J. Sjöstrand (1980)
Propagation of analytic singularities for second order dirichlet problemsCommunications in Partial Differential Equations, 5
-
R. Melrose (1975)
Local Fourier-Airy integral operatorsDuke Mathematical Journal, 42
-
P. Laubin (1987)
Etude 2-microlocale de la diffractionBull. Soc. Roy. Sc. Liège, 4
-
J. Sjöstrand (1982)
Singularités analytiques microlocalesAstérisque, 95
- Publisher
- Springer Journals
- Copyright
- Copyright © Università degli Studi di Ferrara 1999
- ISSN
- 0430-3202
- eISSN
- 1827-1510
- DOI
- 10.1007/bf02826095
- Publisher site
- See Article on Publisher Site
Abstract
Ann. Univ. Ferrara - Sez. VII - Sc. Mat. Suppl. Vol. XLV, 197-211 (1999) On the Lagrangian Regularity Near non-Transversal Crossing of Lagrangian Manifolds. PASCAL LAUBIN (*) To tt~e memory of Lamberto Cattabriga 1. - Introduction. In [12], a class of lagrangian distributions associated to a pair of conic la- grangian submanifolds with transversal crossing is used to construct in the C~ framework a parametrix of the Cauchy problem for an operator with multiple involutive characteristics. In this paper, we review a more general construc- tion in the Co and analytic category using some ideas from second microlocal- ization. An application is given to the lagrangian properties of the solution at the transition from the shadow to the illuminated region in diffraction theory. First in the C~ framework and using the canonical invariance, we prove that the solution belongs to a class of lagrangian distributions associated to a pair of lagrangian submanifolds. As a consequence, we see that, for a conormal data, the second wave front lies in a lagrangian submanifold. We next investigate the same problem in the analytic category. Here we use the geometry of complex canonical transforms and the H~ spaces of SjSs- trand. We generalize
Journal
ANNALI DELL UNIVERSITA DI FERRARA – Springer Journals
Published: Jan 1, 1999
Keywords: Cotangent Bundle; Principal Symbol; Lagrangian Submanifolds; Lagrangian Manifold; Microlocal Analysis