Increasing Stability of the Continuation for the Maxwell System. Deepak Aralumallige Subbarayappa and Victor Isakov

In this paper we obtain bounds showing increasing stability of the continuation for solutions of the stationary Maxwell system when the wave number k is growing. We use a reduction of this system to a new system with the Helmholtz operator in the principal part and use hyperbolic energy and Carleman estimates with k-independent constants in the Cauchy problem for this equations. Hyperbolic energy estimates suggest an existence of increasing (with k) subspaces where the solution of the Cauchy problem is Lipschitz stable disregard of any (pseudo) convexity assumptions.