Continuous Observability for the Anisotropic Maxwell System

A boundary observability inequality for the homogeneous Maxwell system with variable, anisotropic coefficients is proved. The result implies uniqueness for an ill-posed Cauchy problem for Maxwell's system. Both results are so far known only in the special case of isotropic coefficients, i.e., when Maxwell's system reduces to a vector wave equation. Here the analysis has been carried out for the first-order system directly without references to the wave equation.