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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Conditional stability estimation for an inverse boundary problem with non-smooth boundary in $\mathcal {R}^3$
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by J. Cheng, Y. C. Hon and M. Yamamoto PDF
Trans. Amer. Math. Soc. 353 (2001), 4123-4138 Request permission

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
  • MR Author ID: 231929
  • Email: myama@ms.u-tokyo.ac.jp
  • 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).
  • © Copyright 2001 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 353 (2001), 4123-4138
  • MSC (1991): Primary 35R30, 31B20
  • DOI: https://doi.org/10.1090/S0002-9947-01-02758-1
  • MathSciNet review: 1837223