This paper deals with linear PDE with multiple characteristics; the principal symbol is assumed to be elliptic in a certain set of variables, and some conditions are imposed on the lower order terms. The local solvability is then proved for such operators in mixed Gevrey-$C^\infty$ classes, in the sense that the datum is allowed to be $C^\infty$ in some variables, but it is forced to be Gevrey in the other ones.
Notes on the Local Solvability for Partial Differential Equations with Multiple Characteristics in Mixed Gevrey-$C^infty$ Spaces
OLIARO, Alessandro
2005-01-01
Abstract
This paper deals with linear PDE with multiple characteristics; the principal symbol is assumed to be elliptic in a certain set of variables, and some conditions are imposed on the lower order terms. The local solvability is then proved for such operators in mixed Gevrey-$C^\infty$ classes, in the sense that the datum is allowed to be $C^\infty$ in some variables, but it is forced to be Gevrey in the other ones.
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