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

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. 
@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},
     publisher = {mathdoc},
     volume = {Ser. 8, 9B},
     number = {3},
     year = {2006},
     zbl = {1121.35029},
     mrnumber = {2274114},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a4/}
}
TY  - JOUR
AU  - De Donno, Giuseppe
AU  - Oliaro, Alessandro
TI  - Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity
JO  - Bollettino della Unione matematica italiana
PY  - 2006
SP  - 583
EP  - 610
VL  - 9B
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a4/
LA  - en
ID  - BUMI_2006_8_9B_3_a4
ER  - 
%0 Journal Article
%A De Donno, Giuseppe
%A Oliaro, Alessandro
%T Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity
%J Bollettino della Unione matematica italiana
%D 2006
%P 583-610
%V 9B
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/BUMI_2006_8_9B_3_a4/
%G en
%F BUMI_2006_8_9B_3_a4
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/