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On the injectivity and linearization of the coefficient-to-solution mapping for elliptic boundary value problems. (English) Zbl 0817.35021

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.

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
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