Geodesic
Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity
Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 583-610

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

Zbl MR
We propose a unified approach, based on methods from microlocal analysis, for characterizing the hypoellipticity and the local solvability in $C^\infty$ and Gevrey $G^\lambda$ classes of semilinear anisotropic partial differential operators with Gevrey nonlinear perturbations, in dimension $n \geq 3$. The conditions for our results are imposed on the sign of the lower order terms of the linear part of the operator, see Theorem 1.1 and Theorem 1.3 below. 
De Donno, Giuseppe; Oliaro, Alessandro. Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity. Bollettino della Unione matematica italiana, Série 8, 9B (2006) no. 3, pp. 583-610. http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a4/
@article{BUMI_2006_8_9B_3_a4,
     author = {De Donno, Giuseppe and Oliaro, Alessandro},
     title = {Hypoellipticity and local solvability of anisotropic {PDEs} with {Gevrey} nonlinearity},
     journal = {Bollettino della Unione matematica italiana},
     pages = {583--610},
     year = {2006},
     volume = {Ser. 8, 9B},
     number = {3},
     zbl = {1121.35029},
     mrnumber = {2274114},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a4/}
}
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