Propagation des singularités pour les opérateurs différentiels de type principal localement résolubles à coefficients analytiques en dimension 2
Annales de l'Institut Fourier, Volume 29 (1979) no. 2, p. 223-245
On a paracompact analytic manifold of dimension 2, one considers a differential operator P with analytic principal symbol p m satisfying the condition (𝒫) 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 (0), along the integral leaves of the differential system generated by the Hamiltonian vector fields of Rep m and Imp m .
Sur une variété analytique paracompacte de dimension 2, on considère un opérateur différentiel P à symbole principal p m analytique vérifiant la condition (𝒫) 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 (0), le long des feuilles intégrales du système différentiel engendré par les champs hamiltoniens de Rep m et Imp m .
@article{AIF_1979__29_2_223_0,
     author = {Godin, Paul},
     title = {Propagation des singularit\'es pour les op\'erateurs diff\'erentiels de type principal localement r\'esolubles \`a coefficients analytiques en dimension 2},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {29},
     number = {2},
     year = {1979},
     pages = {223-245},
     doi = {10.5802/aif.748},
     zbl = {0365.58019},
     mrnumber = {81m:35024},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1979__29_2_223_0}
}
Godin, Paul. Propagation des singularités pour les opérateurs différentiels de type principal localement résolubles à coefficients analytiques en dimension 2. Annales de l'Institut Fourier, Volume 29 (1979) no. 2, pp. 223-245. doi : 10.5802/aif.748. http://www.numdam.org/item/AIF_1979__29_2_223_0/

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