New global stability estimates for the Calderón problem in two dimensions
نویسندگان
چکیده
We prove a new global stability estimate for the Gel’fandCalderón inverse problem on a two-dimensional bounded domain. Specifically, the inverse boundary value problem for the equation −∆ψ+v ψ = 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 more a potential is smooth, the more its reconstruction is stable. Furthermore, the stability is proven to depend exponentially on the smoothness, in a sense to be made precise. As a corollary we obtain a similar estimate for the Calderón problem for the electrical impedance tomography.
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