Abstract and Applied Analysis
Volume 2004 (2004), Issue 7, Pages 625-634

The operator B*L for the wave equation with Dirichlet control

I. Lasiecka and R. Triggiani

Department of Mathematics, University of Virginia, Kerchof Hall, Charlottesville 22904, VA, USA

Received 26 April 2004

Copyright © 2004 I. Lasiecka and R. Triggiani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the case of the wave equation, defined on a sufficiently smooth bounded domain of arbitrary dimension, and subject to Dirichlet boundary control, the operator B*L from boundary to boundary is bounded in the L2-sense. The proof combines hyperbolic differential energy methods with a microlocal elliptic component.