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An identification problem for an elliptic equation in two variables. (English) Zbl 0662.35118
We consider the elliptic equation div(a(x)grad u(x))\(=0\), \(x\in \Omega\), in which the coefficient a has to be determined when one solution u is known. Here \(\Omega\) is a bounded smooth domain in \({\mathbb{R}}^ 2\). This is a nonlinear ill-posed problem of identification. The results which are of main interest are uniqueness, stability and algorithms.

MSC:
35R30 Inverse problems for PDEs
35R25 Ill-posed problems for PDEs
35J60 Nonlinear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
35B35 Stability in context of PDEs
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