WIAS Preprint No. 2351, (2016)

Single logarithmic conditional stability in determining unknown boundaries



Authors

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

2010 Mathematics Subject Classification

  • 35R30 74B05 78A46

Keywords

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

DOI

10.20347/WIAS.PREPRINT.2351

Abstract

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.

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