New global stability estimates for the Calderón problem in two dimensions

Details New global stability estimates for the Calderón problem in two dimensions New global stability estimates for the Calderón problem in two dimensions

2011-10-03

arxiv.org/abs/1110.0335v2

Mathematics

Analysis of PDEs

18 pages

Scientific paper

We prove a new global stability estimate for the Gel'fand-Calder\'on inverse problem on a two-dimensional bounded domain or, more precisely, the inverse boundary value problem for the equation $-\Delta \psi + v\, \psi = 0$ on $D$, where $v$ is a smooth real-valued potential of conductivity type defined on a bounded planar domain $D$. The principal feature of this estimate is that it shows that the more a potential is smooth, the more its reconstruction is stable, and the stability varies exponentially with respect to the smoothness (in a sense to be made precise). As a corollary we obtain a similar estimate for the Calder\'on problem for the electrical impedance tomography.

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