Journal of Inequalities and Applications 
Volume 4 (1999), Issue 4, Pages 283-299
doi:10.1155/S1025583499000405

Some generalized Poincaré inequalities and applications to problems arising in electromagnetism

Roberta Nibbi

 Dipartimento di Matematica, Università di Bologna, Piazza di Porta San Donato 5, Bologna 40127, Italy
Received 30 September 1998; Revised 16 January 1999

Abstract

Two Poincaré type theorems for sufficiently regular fields are obtained. In particular, we prove that their L2(Ω)-norm can be controlled by the L2(Ω)-norms of their curl and divergence and the L2(∂Ω)-norm of their tangential (or normal) component on the boundary. Finally, some applications of these results are given in the context of the electromagnetic theory.