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Applicable Analysis
An International Journal
Volume 99, 2020 - Issue 5
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Articles

Single logarithmic conditional stability in determining unknown boundaries

Johannes ElschnerWeierstrass Institute, Berlin, GermanyView further author information
,
Guanghui HuBeijing Computational Science Research Center, Beijing, People's Republic of ChinaCorrespondence[email protected]
View further author information
&
Masahiro YamamotoDepartment of Mathematical Sciences, University of Tokyo, Tokyo, Japan;Center of Nonlinear Problems of Mathematical Physics, Peoples' Friendship University of Russia, Moscow, RussiaView further author information
Pages 725-746 | Received 18 Mar 2018, Accepted 26 Jul 2018, Published online: 28 Aug 2018
 
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ABSTRACT

We prove a conditional stability estimate of log-type for determining unknown boundaries from a single Cauchy data taken on an accessible sub-boundary. Our approach relies on new interior and boundary estimates for elliptic equations which are derived from the Carleman estimate. Stability results for target identification of an acoustic sound-soft scatterer from one or several far-field patterns are also obtained.

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No potential conflict of interest was reported by the authors.

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Funding

Masahiro Yamamoto is partly supported by Grant-in-Aid for Scientific Research (S) 15H05740 of Japan Society for the Promotion of Science and by the Ministry of Education and Science of the Russian Federation (the Agreement number No.02.a03.21.0008).

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