Identification of an Unknown Parameter Function in the Main Part of an Elliptic Partial Differential Equation

Abstract

The identification of an unknown parameter function in the main part of an elliptic partial differential equation is studied. We use a Tichonov regularization with an $H^s$-norm and $s>0$. Moreover, pointwise bounds for the unknown parameter are assumed. Existence of solutions is shown and necessary optimality conditions are established. The main contribution is the discussion of second-order sufficient optimality conditions. Here, we get a size condition of the parameter $s$.