Monotonicity-based inversion of the fractional Schrödinger equation I. Positive potentials

Bastian Harrach, Yi Hsuan Lin

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

We consider an inverse problem for the fractional Schrödinger equation by using monotonicity formulas. We provide if-and-only-if monotonicity relations between positive bounded potentials and their associated nonlocal Dirichlet-to-Neumann maps. Based on the monotonicity relation, we can prove uniqueness for the nonlocal Calderón problem in a constructive manner. Second, we offer a reconstruction method for unknown obstacles in a given domain. Our method is independent of the dimension and only requires the background solution of the fractional Schrödinger equation.

Original languageEnglish
Pages (from-to)3092-3111
Number of pages20
JournalSIAM Journal on Mathematical Analysis
Volume51
Issue number4
DOIs
StatePublished - 2019

Keywords

  • Calderón’s problem
  • Fractional Schrödinger equation
  • Inverse obstacle problem
  • Localized potentials
  • Monotonicity method
  • Runge approximation property
  • Shape reconstruction

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