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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Conditional stability estimation for an inverse boundary problem with non-smooth boundary in $\mathcal{R}^3$


Authors: J. Cheng, Y. C. Hon and M. Yamamoto
Journal: Trans. Amer. Math. Soc. 353 (2001), 4123-4138
MSC (1991): Primary 35R30, 31B20
Published electronically: June 6, 2001
MathSciNet review: 1837223
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Abstract:

In this paper, we investigate an inverse problem of determining a shape of a part of the boundary of a bounded domain in $\mathcal R^3$ 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.


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Additional Information

J. Cheng
Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, China & Department of Mathematics, Faculty of Engineering, Gunma University, Kiryu 376-8515, Japan
Email: jcheng@math.sci.gunma-u.ac.jp and jcheng@fudan.edu.cn

Y. C. Hon
Affiliation: Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Email: maychon@cityu.edu.hk

M. Yamamoto
Affiliation: Department of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan
Email: myama@ms.u-tokyo.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02758-1
PII: S 0002-9947(01)02758-1
Keywords: Determination of unknown boundary, conditional stability estimation, non-smooth boundary
Received by editor(s): July 27, 1999
Received by editor(s) in revised form: June 16, 2000
Published electronically: June 6, 2001
Additional Notes: The first author is partly supported by NSF of China (No.19971016). This work was also partially supported by the Research Grants Council of the Hong Kong SAR,China (Grant numbers #9040428) and the Sanwa Systems Development Company Limited (Tokyo, Japan).
Article copyright: © Copyright 2001 American Mathematical Society