JournalszaaVol. 32, No. 2pp. 163–178

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

  • Ute Aßmann

    Universität Duisburg-Essen, Germany
  • Arnd Rösch

    Universität Duisburg-Essen, Germany
Identification of an Unknown Parameter Function in the Main Part of an Elliptic Partial Differential Equation cover
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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 HsH^s-norm and s>0s>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 ss.

Cite this article

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

DOI 10.4171/ZAA/1479