We consider a class of semilinear partial differential equations whose linear part is the power of an anisotropic operator in $n$ variables and whose nonlinear term is allowed to be non analytic with respect both to the variables and the covariables; for such equations we prove local solvability in Gevrey classes. We shall mention, in the last Section, a possible generalisation of this result to mixed Gevrey-$C^\infty$ classes.
Local solvability for powers of anisotropic operators
OLIARO, Alessandro
2007-01-01
Abstract
We consider a class of semilinear partial differential equations whose linear part is the power of an anisotropic operator in $n$ variables and whose nonlinear term is allowed to be non analytic with respect both to the variables and the covariables; for such equations we prove local solvability in Gevrey classes. We shall mention, in the last Section, a possible generalisation of this result to mixed Gevrey-$C^\infty$ classes.
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