New global stability estimates for the Calderón problem in two dimensions

Abstract

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.

18 pages

References in corpus (3)

• Lipschitz stability for the electrical impedance tomography problem: the complex case
• A global stability estimate for the Gel'fand-Calderon inverse problem in two dimensions
• New global stability estimates for the Gel'fand-Calderon inverse problem

Cited by in corpus (4)

• Stability and uniqueness for a two-dimensional inverse boundary value problem for less regular potentials
• Stability estimates for an inverse problem for the Schrödinger equation at negative energy in two dimensions
• On the Calderòn problem in periodic cylindrical domain with partial Dirichlet and Neumann data
• Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map