Identification of an unknown parameter function in the main part of an elliptic partial differential equation
type: Item
instance of: scholarly article
title: Identification of an unknown parameter function in the main part of an elliptic partial differential equation
zbMATH Open document ID: 1264.35278
DOI: 10.4171/ZAA/1479
author: Ute Aßmann
author: Arnd Rösch
published in: Zeitschrift für Analysis und ihre Anwendungen
publication date: 2013-05-28T00:00:00Z
review text: 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 \(s\).
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 49N45
Mathematics Subject Classification ID: 49K20
Mathematics Subject Classification ID: 49J20
zbMATH DE Number: 6167079
zbMATH Keywords: parameter identification
zbMATH Keywords: inverse problems
zbMATH Keywords: Tichonov regularization
zbMATH Keywords: optimal control
zbMATH Keywords: inequality constraints
zbMATH Keywords: necessary and sufficient optimality conditions
Wikidata QID: Q115211759
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.4171/zaa/1479
OpenAlex ID: W1970741631
description: scientific article; zbMATH DE number 6167079