Sur une variété analytique paracompacte de dimension 2, on considère un opérateur différentiel à symbole principal analytique vérifiant la condition 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 , dans , le long des feuilles intégrales du système différentiel engendré par les champs hamiltoniens de Re et Im.
On a paracompact analytic manifold of dimension 2, one considers a differential operator with analytic principal symbol satisfying the condition 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 , in , along the integral leaves of the differential system generated by the Hamiltonian vector fields of Re and Im.
@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}, volume = {29}, year = {1979}, pages = {223-245}, doi = {10.5802/aif.748}, mrnumber = {81m:35024}, zbl = {0365.58019}, language = {fr}, url = {http://dml.mathdoc.fr/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, Tome 29 (1979) pp. 223-245. doi : 10.5802/aif.748. http://gdmltest.u-ga.fr/item/AIF_1979__29_2_223_0/
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