Lipschitz stability in inverse parabolic problems by the Carleman estimate

Abstract

We consider a system with a suitable boundary condition, where is a bounded domain, is a uniformly elliptic operator of the second order whose coefficients are suitably regular for , is fixed, and a function satisfies Our inverse problems are determinations of g using overdetermining data or , where and . Our main result is the Lipschitz stability in these inverse problems. We also consider the determination of , in the case of with given R satisfying on . Finally, we discuss an upper estimation of our overdetermining data by means of f.