Conditional stability estimation for an inverse boundary problem with non-smooth boundary in R3

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Author(s)

  • J. Cheng
  • Y. C. Hon
  • M. Yamamoto

Related Research Unit(s)

Detail(s)

Original languageEnglish
Pages (from-to)4123-4138
Journal / PublicationTransactions of the American Mathematical Society
Volume353
Issue number10
Publication statusPublished - 2001

Abstract

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. © 2001 American Mathematical Society.

Research Area(s)

  • Conditional stability estimation, Determination of unknown boundary, Non-smooth boundary