Appl Math Optim 54:47–70 (2006)
2006 Springer Science+Business Media, Inc.
Internal and Boundary Observability Estimates
for the Heterogeneous Maxwell’s System
and Cristina Pignotti
Universit´e de Valenciennes et du Hainaut Cambr´esis,
MACS, Institut des Sciences et Techniques de Valenciennes,
59313 Valenciennes Cedex 9, France
Dipartimento di Matematica Pura e Applicata, Universit`a di L’Aquila,
Via Vetoio, Loc. Coppito, 67010 L’Aquila, Italy
Communicated by Irene Lasiecka
Abstract. Observability estimates for Maxwell’s system with variable coefﬁcients
are established using the differential geometry method recently developed for scalar
wave equations. The main tool is that Maxwell’s system is reducible to a perturbed
vectorial wave equation with a decoupled principal part.
Key Words. Maxwell’s system, Observability estimates.
AMS Classiﬁcation. 93D15, 93D05, 93C20.
The exact boundary controllability and stabilization of Maxwell’s equations with con-
stant coefﬁcients have been studied by many authors , , , , , , ,
,  and are usually based on an observability estimate obtained by different meth-
ods like the multiplier method, microlocal analysis and the frequency domain method.
A similar strategy lead to the internal controllability of Maxwell’s equations, see for
instance , , , and .
More recently, several papers were devoted to the stability and/or controllability
of Maxwell’s system with variable coefﬁcients , , , –. All of them