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
;
2008-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
