The ill-posed Cauchy problem by Controllability the elliptic case

In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. To do this, interpret as inverse problem, and therefore a controllability problem. This point of view induces regularization method that makes it possible, on one hand, to characterize existence regular solution On other possible obtain singular optimality system optimal control, without resorting any additional assumption, such non-vacuity interior sets admissibles controls, assumption many analysis have had use. From view, presented here, called method, is original analyzed