Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity
De Donno, Giuseppe ; Oliaro, Alessandro
Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 583-610 / Harvested from Biblioteca Digitale Italiana di Matematica
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We propose a unified approach, based on methods from microlocal analysis, for characterizing the hypoellipticity and the local solvability in C∞ and Gevrey Gλ classes of semilinear anisotropic partial differential operators with Gevrey nonlinear perturbations, in dimension n≥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.

In questo articolo viene proposto un approccio unificato, che si basa sulle tecniche dell'analisi microlocale, per caratterizzare sia l'ipoellitticità sia la risolubilità locale, in C∞ e nelle classi di Gevrey Gλ, di operatori alle derivate parziali anisotropi, in dimensione n≥3, i quali, vengono perturbati con non linearità di tipo Gevrey. Per ottenere questi risultati sono state imposte alcune condizioni sul segno dei termini di ordine inferiore della parte lineare dell'operatore, vedere Teorema 1.1 e Teorema 1.3.

Publié le : 2006-10-01
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     author = {Giuseppe De Donno and Alessandro Oliaro},
     title = {Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {583-610},
     zbl = {1121.35029},
     mrnumber = {2274114},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_3_583_0}
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De Donno, Giuseppe; Oliaro, Alessandro. Hypoellipticity and local solvability of anisotropic PDEs with Gevrey nonlinearity. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 583-610. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_3_583_0/

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