In this paper we prove two results on the Levi conditions for weakly hyperbolic systems with characteristics of constant multiplicities. A first result concerns scalar operators: we prove that Levi conditions defined by the second author in (C. R. Acad. Sc. Paris 1991) are equivalent to the usual Levi conditions for scalar operator. A second result concerns systems whose principal symbol has a Jordan form made of a large number of 2x2 blocks. For these systems we express the first Levi condition via an invariant constructed from the sub-characteristic matrix. Moreover we show that this condition is necessary for the C-infinity well-posedness.

Remarks on the Levi conditions for differential systems

TAGLIALATELA, Giovanni
;
2008

Abstract

In this paper we prove two results on the Levi conditions for weakly hyperbolic systems with characteristics of constant multiplicities. A first result concerns scalar operators: we prove that Levi conditions defined by the second author in (C. R. Acad. Sc. Paris 1991) are equivalent to the usual Levi conditions for scalar operator. A second result concerns systems whose principal symbol has a Jordan form made of a large number of 2x2 blocks. For these systems we express the first Levi condition via an invariant constructed from the sub-characteristic matrix. Moreover we show that this condition is necessary for the C-infinity well-posedness.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/72692
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