New global stability estimates for the Calderón problem in two dimensions

Matteo Santacesaria (1)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We prove a new global stability estimate for the Gel'fand-Calderón 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 Calderón problem for the electrical impedance tomography.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Matteo Santacesaria. New global stability estimates for the Calderón problem in two dimensions. Journal of the Institute of Mathematics of Jussieu, 2013, 12 (3), pp.553-569. ⟨10.1017/S147474801200076X⟩. ⟨hal-00628403v2⟩