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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.
Additional information
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).