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Conditional stability estimation for an inverse boundary problem with non-smooth boundary in 
Author(s):
J.
Cheng;
Y.
C.
Hon;
M.
Yamamoto
Journal:
Trans. Amer. Math. Soc.
353
(2001),
4123-4138.
MSC (1991):
Primary 35R30, 31B20
Posted:
June 6, 2001
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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  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:
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
Posted:
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).
Copyright of article:
Copyright
2001,
American Mathematical Society
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