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 journalArticle

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

Fingerprint

Lipschitz Stability
Inverse Boundary Value Problem
Dirichlet-to-Neumann Map
Schrodinger Equation
Stability Estimates
Convergence of numerical methods
Ill-posed Problem
Boundary value problems
Lipschitz
Logarithmic
Schrodinger equation
Unknown
Knowledge

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics
  • Computational Mathematics

Cite this

Lipschitz stability of an inverse boundary value problem for a schro dinger-type equation. / Beretta, Elena; De Hoop, Maarten V.; Qiu, Lingyun.

In: SIAM Journal on Mathematical Analysis, Vol. 45, No. 2, 10.07.2013, p. 679-699.

Research output: Contribution to journalArticle

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