83 research outputs found
Counterexamples to well posedness for some hyperbolic operators with triple characteristics
In this paper we prove that for a class of non-effectively hyperbolic
operators with smooth triple characteristics the Cauchy problem is well posed
in the Gevrey 2 class, beyond the generic Gevrey class (see e.g.
\cite{Bro}). Moreover we show that this value is optimal
On The Cauchy Problem for Non Effectively Hyperbolic Operators, The Ivrii-Petkov-Hörmander Condition and the Gevrey Well Posedness
2000 Mathematics Subject Classification: 35L15, Secondary 35L30.In this paper we prove that for non effectively hyperbolic operators with smooth double characteristics with the Hamilton map exhibiting
a Jordan block of size 4 on the double characteristic manifold the Cauchy
problem is well posed in the Gevrey 6 class if the strict Ivrii-Petkov-Hörmander condition is satisfied
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