Conditional stability estimation for an inverse boundary problem with non-smooth boundary in

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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9947-01-02758-1

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