Abstract and Applied Analysis
Volume 2004 (2004), Issue 7, Pages 625-634
The operator for the wave equation with
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 from boundary to boundary is
bounded in the -sense. The proof combines hyperbolic
differential energy methods with a microlocal elliptic component.