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 \(\Omega\).


58J47 Propagation of singularities; initial value problems on manifolds
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