Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case
Lipschitz Stability for the Electrical Impedance Tomography Problem: The Complex Case
复制标题
电阻抗断层扫描问题的 Lipschitz 稳定性：复杂案例
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
E. Francini
中科院分区：
文献类型：
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作者：
E. Beretta;E. Francini
本文研究了一类边值问题，其中γ为复值L∞系数，满足强椭圆性条件。在电阻抗断层扫描中，γ表示导电体的导纳。一个有趣的问题是从狄利克雷-诺伊曼图Λγ的知识中唯一而稳定地确定γ的问题。在上述一般假设下，这个问题是一个悬而未决的问题。在本文中，我们证明了，如果我们先验地假设γ是分段常数，并且已知未知值的数目有限，那么从Λγ出发的γ的Lipschitz连续性成立。
In this article we investigate the boundary value problem where γ is a complex valued L ∞ coefficient, satisfying a strong ellipticity condition. In electrical impedance tomography, γ represents the admittance of a conducting body. An interesting issue is the one of determining γ uniquely and in a stable way from the knowledge of the Dirichlet-to-Neumann map Λγ. Under the above general assumptions this problem is an open issue. In this article we prove that, if we assume a priori that γ is piecewise constant with a bounded known number of unknown values, then Lipschitz continuity of γ from Λγ holds.