On Runge approximation and Lipschitz stability for a finite-dimensional Schrödinger inverse problem

ABSTRACT

In this note we reprove the Lipschitz stability for the inverse problem for the Schrödinger operator with finite-dimensional potentials by using quantitative Runge approximation results. This provides a quantification of the Schrödinger version of the argument from Kohn and Vogelius [Determining conductivity by boundary measurements. II. Interior results. Comm Pure Appl Math. 1985;38(5):643–667] and presents a slight variant of the strategy considered in Alessandrini et al. [Lipschitz stability for a piecewise linear Schrödinger potential from local Cauchy data. Asymptotic Anal. 2018;108:115–149] which may prove useful also in the context of more general operators.

Keywords:

• Runge approximation
• Lipschitz stability
• Schrödinger equation

2010 Mathematics Subject Classification:

• 35R30

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work of ES was performed under the PRIN grant No. 201758MTR2-007. ES has also been supported by the Individual Funding for Basic Research (FFABR) granted by MIUR.