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.
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