Conditional stability estimate for an ill-posed elliptic equation by using nonlocal conditions

Conditional stability for ill - posed elliptic Cauchy problems : the case of Lipschitz domains ( part II )

This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace’s equation in domains with Lipschitz boundary. It completes the results obtained in [4] for domains of class C. This estimate is established by using an interior Carleman estimate and a technique based on a sequence of balls which approach the boundary. This technique is inspired f...

Conditional Stability Estimates for Ill-posed Pde Problems by Using Interpolation

The focus of this paper is on conditional stability estimates for illposed inverse problems in partial differential equations. Conditional stability estimates have been obtained in the literature by a couple different methods. In this paper we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We are going to work out the theoretical backgr...

Optimal Control of an Ill Posed Elliptic Semilinear Equation with an Exponential Non Linearity

We study here an optimal control problem for a semilinear elliptic equation with an exponential nonlinearity such that we cannot expect to have a solution of the state equation for any given control We then have to speak of pairs control state After having de ned a suit able functional class in which we look for solutions we prove existence of an optimal pair for a large class of cost functions...

Conditional stability for ill - posed elliptic Cauchy problems : the case of C 1 , 1 domains ( part I )

This paper is devoted to a conditional stability estimate related to the ill-posed Cauchy problems for the Laplace’s equation in domains with C boundary. It is an extension of an earlier result of [19] for domains of class C. Our estimate is established by using a global Carleman estimate near the boundary in which the exponential weight depends on the distance function to the boundary. Further...

A Conditional Stability Estimate for an Inverse Neumann Boundary Problem