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New global stability estimates for the Calderón problem in two dimensions
- Part of
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- Journal:
- Journal of the Institute of Mathematics of Jussieu / Volume 12 / Issue 3 / July 2013
- Published online by Cambridge University Press:
- 07 June 2012, pp. 553-569
- Print publication:
- July 2013
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- Article
- Export citation
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We prove a new global stability estimate for the Gel’fand–Calderón inverse problem on a two-dimensional bounded domain. Specifically, the inverse boundary value problem for the equation
${- }\Delta \psi + v\hspace{0.167em} \psi = 0$ on 
$D$ is analysed, where 
$v$ is a smooth real-valued potential of conductivity type defined on a bounded planar domain 
$D$. The main feature of this estimate is that it shows that the smoother a potential is, the more stable its reconstruction is. Furthermore, the stability is proven to depend exponentially on the smoothness, in a sense to be made precise. The same techniques yield a similar estimate for the Calderón problem for electrical impedance tomography.
