Ito, K.; Kunisch, K. On the injectivity and linearization of the coefficient-to-solution mapping for elliptic boundary value problems. (English) Zbl 0817.35021 J. Math. Anal. Appl. 188, No. 3, 1040-1066 (1994). 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. Reviewer: M.Perelmuter (Kiev) Cited in 12 Documents MSC: 35J25 Boundary value problems for second-order elliptic equations 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs Keywords:coefficient-to-solution mapping; injectivity; linearization PDF BibTeX XML Cite \textit{K. Ito} and \textit{K. Kunisch}, J. Math. Anal. Appl. 188, No. 3, 1040--1066 (1994; Zbl 0817.35021) Full Text: DOI OpenURL