Identification of an unknown parameter function in the main part of an elliptic partial differential equation
Summary: 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 \(s\).
necessary and sufficient optimality conditions
scientific article; zbMATH DE number 6167079