Propagation des singularités pour les opérateurs différentiels de type principal localement résolubles à coefficients analytiques en dimension 2

Godin, Paul

Annales de l'Institut Fourier, Tome 29 (1979) no. 2, pp. 223-245.

Sur une variété analytique paracompacte de dimension 2, on considère un opérateur différentiel $P$ à symbole principal $p_m$ analytique vérifiant la condition $\left(𝒫\right)$ de Nirenberg et Treves. En ajoutant une nouvelle variable et en utilisant des estimations a priori de type Carleman, on montre qu’il y a propagation des singularités pour $P$, dans $p_m^{-1}\left(0\right)$, le long des feuilles intégrales du système différentiel engendré par les champs hamiltoniens de Re$p_m$ et Im$p_m$.

On a paracompact analytic manifold of dimension 2, one considers a differential operator $P$ with analytic principal symbol $p_m$ satisfying the condition $\left(𝒫\right)$ of Nirenberg and Treves. Adding a new variable and using a priori estimates of Carleman type, one shows that there is propagation of singularities for $P$, in $p_m^{-1}\left(0\right)$, along the integral leaves of the differential system generated by the Hamiltonian vector fields of Re$p_m$ and Im$p_m$.

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