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Zeitschrift für Analysis und ihre Anwendungen


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Volume 32, Issue 2, 2013, pp. 163–178
DOI: 10.4171/ZAA/1479

Published online: 2013-04-08

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

Ute Aßmann[1] and Arnd Rösch[2]

(1) Universität Duisburg-Essen, Germany
(2) Universität Duisburg-Essen, Germany

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 $s$.

Keywords: Parameter identification, inverse problems, Tichonov regularization, optimal control, inequality constraints, necessary and sufficient optimality conditions

Aßmann Ute, Rösch Arnd: Identification of an Unknown Parameter Function in the Main Part of an Elliptic Partial Differential Equation. Z. Anal. Anwend. 32 (2013), 163-178. doi: 10.4171/ZAA/1479