581 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
Cauchy problem for hyperbolic operators with triple characteristics of variable multiplicity
We study a class of third order hyperbolic operators in with triple characteristics on
. We consider the case when the fundamental matrix of the principal
symbol for has a couple of non vanishing real eigenvalues and is
strictly hyperbolic for We prove that is strongly hyperbolic, that
is the Cauchy problem for is well posed in for any lower order
terms
Propagation of singularities for hyperbolic operators with multiple involutive characteristics
Higher secant varieties of embedded in bi-degree
Let denote the Segre-Veronese embedding of via the sections of the sheaf . We study
the dimensions of higher secant varieties of and we prove
that there is no defective secant variety, except possibly for
values of . Moreover when is multiple of , the
secant variety of has the expected dimension for
every .Comment: 8 page
On an ODE Relevant for the General Theory of the Hyperbolic Cauchy Problem
2000 Mathematics Subject Classification: 34E20, 35L80, 35L15.In this paper we study an ODE in the complex plane. This is a key step in the search of new necessary conditions for the well posedness of the Cauchy Problem for hyperbolic operators with double characteristics
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