Local solvability for powers of anisotropic operators

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 nonanalytic 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 generalization of this result to mixed Gevrey-C ^∞ classes.

Keywords:

• Local solvability
• Anisotropic operators
• Gevrey classes
• Semilinear equations

Keywords:

• AMS 2000 Mathematics Subject Classifications:
• 35S05
• 42B10