## 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 |
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MSC(Secondary) | |

Uncontrolled Keywords | Cauchy problem for systems with constant multiplicities, Levi conditions. |