In this paper we study the local solvability in Gevrey classes for degenerate parabolic operators of order $\geq 2$. We assume that the lower order term vanishes at a suitably smaller rate with respect to the principal part; we then analyze its influence on the behaviour of the operator, proving local solvability in Gevrey spaces $G^s$ for small $s$, and local nonsolvability in $G^s$ for large $s$.
Gevrey Local Solvability for DegenerateParabolic Operators of Higher Order
OLIARO, Alessandro;
2007-01-01
Abstract
In this paper we study the local solvability in Gevrey classes for degenerate parabolic operators of order $\geq 2$. We assume that the lower order term vanishes at a suitably smaller rate with respect to the principal part; we then analyze its influence on the behaviour of the operator, proving local solvability in Gevrey spaces $G^s$ for small $s$, and local nonsolvability in $G^s$ for large $s$.
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