Gevrey Local Solvability for Degenerate Parabolic Operators of Higher Order

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In this paper we study the local solvability in Gevrey classes for degenerate parabolic operators of order ≥ 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 behavior of the operator, proving local solvability in Gevrey spaces G s for small s, and local nonsolvability in G s for large s.