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Deuxième microlocalisation sur les sous variétés isotropes. (French) Zbl 0539.58038
In this paper, we construct the second micro-support of a distribution on \(R^ n\), with respect to an isotropic subvariety \(\Gamma\) of \(T^*R^ n\). It is a closed set in a fiber bundle \({\tilde \Gamma}\) over \(\Gamma\), which is canonically a symplectic variety, and which contains the cotangent bundle of \(\Gamma\). We prove the Watermelon theorem and apply our result to the study of the propagation of singularities of solutions, defined on an open set \(\Omega\), of a differential operator P of real principal type, near a bicharacteristic curve of P, contained in the boundary of \(\Omega\).
Reviewer: Reviewer (Berlin)

MSC:
58J47 Propagation of singularities; initial value problems on manifolds
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References:
[1] J.-M. BONY, Extension du théorème de holmgren, Séminaire Goulaouic-Schwartz, 1975-1976, exposé 17. · Zbl 0336.35003
[2] L. BOUTET de MONVEL, Opérateurs pseudo-différentiels analytiques, Séminaire à Grenoble, 1975-1976.
[3] L. BOUTET de MONVEL, P. KREE, Pseudo-differentiels operators and Gevrey-classes, Ann. Inst. Fourier, 17 (1967), 295-303. · Zbl 0195.14403
[4] L. HÖRMANDER, Fourier integrals operators I, Acta Math., 127 (1971), 70-183. · Zbl 0212.46601
[5] M. KASHIWARA, T. KAWAI, Second microlocalisation and asymptotic expansions, Springer Lec. Notes in Physics, (126), 21-76. · Zbl 0458.46027
[6] K. KATAOKA, Microlocal theory of boundary value problems II, and a theorem on regularity of diffractive operators. · Zbl 0459.35098
[7] Y. LAURENT, Théorie de la deuxième microlocalisation dans le domaine complexe, Thèse, Orsay, 1982. · Zbl 0561.32013
[8] G. LEBEAU, Une propriété d’invariance pour le spectre des traces, C.R.A.S., t. 294 (21 juin 1982), I. 723-725. · Zbl 0508.46032
[9] P. SCHAPIRA, Conditions de positivité dans une variété symplectique complexe. application à l’étude des microfonctions, Ann. Scient. Ec. Norm. Sup., 4e Série, 14 (1981), 121-139. · Zbl 0473.58022
[10] J. SJÖSTRAND, Propagation of analytic singularities for second order Dirichlet problems. I et II, Comm. P.D.E., 5(1) (1980), 41-94 et Comm. P.D.E., 5(2) (1980), 187-207. · Zbl 0534.35030
[11] J. SJÖSTRAND, Singularités analytiques microlocales, Cours à Orsay, (1981).
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