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