Hokkaido Mathematical Journal

TAGLIALATELA Giovanni, VAILLANT Jean,

Remarks on the Levi conditions for differential systems.

Hokkaido Mathematical Journal, 37 (2008) pp.463-492

Fulltext

PDF

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 [29] 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 2 \times 2 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^\infty well-posedness.

MSC(Primary)35L45
MSC(Secondary)
Uncontrolled KeywordsCauchy problem for systems with constant multiplicities, Levi conditions.