Lipschitz stability of an inverse boundary value problem for a schro dinger-type equation

Elena Beretta, Maarten V. De Hoop, Lingyun Qiu

Research output: Contribution to journalArticlepeer-review

27 Scopus citations

Abstract

In this paper we study the inverse boundary value problem of determining the potential in the Schrodinger equation from the knowledge of the Dirichlet-to-Neumann map, which is commonly accepted as an ill-posed problem in the sense that, under general settings, the optimal stability estimate is of logarithmic type. In this work, a Lipschitz-type stability is established assuming a priori that the potential is piecewise constant with a bounded known number of unknown values.

Original languageEnglish (US)
Pages (from-to)679-699
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Volume45
Issue number2
DOIs
StatePublished - Jul 10 2013

Keywords

  • Helmholtz equation
  • Inverse boundary value problem
  • Lipschitz stability
  • Schrodinger equation

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