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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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