Conditional stability estimation for an inverse boundary problem with non-smooth boundary in ℛ³
Conditional stability estimation for an inverse boundary problem with non-smooth boundary in ℛ³
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DOI：
10.1090/s0002-9947-01-02758-1
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发表时间：
2001-06
影响因子：
1.3
通讯作者：
Jin Cheng;Y. Hon;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
Jin Cheng;Y. Hon;Masahiro Yamamoto
本文研究了由拉普拉斯方程的柯西问题的解确定R3中有界区域的部分边界形状的反问题。在未知部分为Lipschitz连续曲面的条件下，给出了在未知部分的合理先验信息下，确定边界部分的对数条件稳定性估计.关键是复扩张和调和测度的估计。
In this paper, we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in R3 by a solution to a Cauchy problem of the Laplace equation. Assuming that the unknown part is a Lipschitz continuous surface, we give a logarithmic conditional stability estimate in determining the part of boundary under reasonably a priori information of an unknown part. The keys are the complex extension and estimates for a harmonic measure.