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Zbl 0539.58038
Lebeau, Gilles
Deuxième microlocalisation sur les sous variétés isotropes. (French)
[J] Ann. Inst. Fourier 35, No.2, 145-216 (1985). ISSN 0373-0956; ISSN 1777-5310/e

In this paper, we construct the second micro-support of a distribution on $R\sp n$, with respect to an isotropic subvariety $\Gamma$ of $T\sp*R\sp n$. 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 $\Omega$.

MSC 2000:: *58J47 Propagation of singularities; initial value problems

Keywords: microlocalisation; differential operator of real principal type; isotropic subvariety; bicharacteristic curve

Cited in: Zbl 0706.35003 Zbl 0644.35006

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