We consider the problem of determining the diffusion coefficient a(x) in a 2D elliptic equation from a distributed measurement z in H~1 of the solution u of the equation. For a problem with a simple geometry, we give conditions under which the first derivative of the b chemical bounds 1/a -> u mapping is coercive. Then we show that its non linearity in a direction d increases, and its sensitivity decreases, when the ratio | integral (d/b)|_L~2/d/b_L~2 increases. THis corroborates observations on scale, sensitivity and non linearity made in (Chavent and Liu, 89) (Grimstad and Mannseth, 99).
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机译：我们考虑从等式的解决方案U中的分布测量Z确定2D椭圆等式中的扩散系数a（x）的问题。对于具有简单几何形状的问题，我们提供了第一个化学界限1 / A - > U映射的第一导数是胁迫的条件。然后，我们表明它在方向D中的非线性增加，并且当比率时，它的灵敏度降低积分（d / b）| _l〜2 / d / b _l〜2增加。这使得对（Chavent和Liu，89）（Grimstad和Mannseth，99）进行了关于规模，敏感性和非线性的观察结果。
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