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.

Hypoellipticity and local solvability of anisotropic PDEs with gevrey nonlinearity

DE DONNO, Giuseppe;OLIARO, Alessandro
2006-01-01

Abstract

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.
2006
9 (8), n. 3
583
610
Semilinear equations; Gevrey spaces; local solvability; hypoellipticity.
G. De Donno; A. Oliaro
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/25815
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