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 -norm and . 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 .
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Ute Aßmann, Arnd Rösch, Identification of an Unknown Parameter Function in the Main Part of an Elliptic Partial Differential Equation. Z. Anal. Anwend. 32 (2013), no. 2, pp. 163–178