WIAS Preprint No. 2351, (2016)

Single logarithmic conditional stability in determining unknown boundaries


  • Elschner, Johannes
  • Hu, Guanghui
  • Yamamoto, Masahiro

2010 Mathematics Subject Classification

  • 35R30 74B05 78A46


  • inverse problems, stability estimate, elliptic equations, Carleman estimate




We prove a conditional stability estimate of log-type for determining unknown boundaries from a single Cauchy data taken on an accessible subboundary. Our approach relies on new interior and boundary estimates derived from the Carleman estimate for elliptic equations. A local stability result for target identification of an acoustic sound-soft scatterer from a single far-field pattern is also obtained.

Appeared in

  • Applicable Analysis, online on 28.08.2018, DOI: https://doi.org/10.1080/00036811.2018.1508654.

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