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Abstract and Applied Analysis
Volume 2004, Issue 7, Pages 625-634
http://dx.doi.org/10.1155/S1085337504404011

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

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

Received 26 April 2004

Copyright © 2004 Hindawi Publishing Corporation. 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.

Abstract

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.