The -dissipativity of first order partial differential operators

Abstract

We find necessary and sufficient conditions for the -dissipativity of the Dirichlet problem for systems of partial differential operators of the first order with complex locally integrable coefficients. As a by-product we obtain sufficient conditions for a certain class of systems of the second order.

Keywords:

• -dissipativity; systems of linear first order partial

AMS Subject Classifications:

• 35F35; 47B44

Acknowledgements

The publication was supported by the Ministry of Education and Science of the Russian Federation (Agreement No. 02.a03.21.0008).

Notes

No potential conflict of interest was reported by the authors.