On the injectivity and linearization of the coefficient-to-solution mapping for elliptic boundary value problems
type: Item
instance of: scholarly article
title: On the injectivity and linearization of the coefficient-to-solution mapping for elliptic boundary value problems
zbMATH Open document ID: 0817.35021
author: Kazufumi Ito
author: Karl Kunisch
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-02-09T00:00:00Z
review text: The authors study the coefficient-to-solution mapping \(a\to a(u)\), where \(u\) is a solution of \(\text{div} (a \text{ grad } u)=f\) in \(\Omega\in \mathbb{R}^ n\), \(n\leq 3\) with \(\Omega\) a bounded domain. A priori estimates for the coefficient \(a\) in terms of \(u\) and injectivity of the mapping \(a\to a(u)\) are derived. The linearization of the coefficient-to-solution mapping is also investigated.
reviewed by: Michael Perelmuter
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35B30
zbMATH DE Number: 720418
zbMATH Keywords: coefficient-to-solution mapping
zbMATH Keywords: injectivity
zbMATH Keywords: linearization
MaRDI profile type: Publication
full work available at URL: jmaa.1994.1479
OpenAlex ID: W1972852525
Wikidata QID: Q123357745
DOI: 10.1006/JMAA.1994.1479
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description: scientific article; zbMATH DE number 720418