Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators
Calvo, Daniela
Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006), p. 21-50 / Harvested from Biblioteca Digitale Italiana di Matematica
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We prove the well-posedness of the Cauchy Problem for first order weakly hyperbolic systems in the multi-anisotropic Gevrey classes, that generalize the standard Gevrey spaces. The result is obtained under the following hypotheses: the principal part is weakly hyperbolic with constant coefficients, the lower order terms satisfy some Levi-type conditions; and lastly the coefficients of the lower order terms belong to a suitable anisotropic Gevrey class. In the proof it is used the quasi-symmetrization of Sylvster-type systems, adapted to the case of the multi-anisotropic Gevrey classes and taking into account the lower order terms.

Si dimostra la buona positura del problema di Cauchy per sistemi debolmente iperbolici nell'ambito delle classi Gevrey multi-anisotrope, generalizzanti le classi Gevrey standard. Il risultato è ottenuto sotto le seguenti ipotesi: la parte principale ha e coefficienti costanti; i termini di ordine inferiore soddisfano delle condizioni di tipo Levi; infine i coefficienti dei termini di ordine inferiore appartengono a un'opportuna classe Gevrey anisotropa. Nella dimostrazione viene utilizzata la tecnica della quasi-simmetrizzazione di sistemi di tipo Sylvester, adattata alle classi Gevrey multi-anisotrope e tenendo conto dei termini di ordine inferiore.

Publié le : 2006-02-01
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     author = {Daniela Calvo},
     title = {Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {9-A},
     year = {2006},
     pages = {21-50},
     zbl = {1178.35236},
     mrnumber = {2204898},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2006_8_9B_1_21_0}
}

Calvo, Daniela. Cauchy problem in multi-anisotropic Gevrey classes for weakly hyperbolic operators. Bollettino dell'Unione Matematica Italiana, Tome 9-A (2006) pp. 21-50. http://gdmltest.u-ga.fr/item/BUMI_2006_8_9B_1_21_0/

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