Global uniqueness for the fractional semilinear schrödinger equation

Ru Yu Lai, Yi-Hsuan Lin

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

We study global uniqueness in an inverse problem for the fractional semilinear Schrödinger equation (-Δ)su + q(x, u) = 0 with s ε (0, 1). We show that an unknown function q(x, u) can be uniquely determined by the Cauchy data set. In particular, this result holds for any space dimension greater than or equal to 2. Moreover, we demonstrate the comparison principle and provide an L estimate for this nonlocal equation under appropriate regularity assumptions.

Original languageEnglish
Pages (from-to)1189-1199
Number of pages11
JournalProceedings of the American Mathematical Society
Volume147
Issue number3
DOIs
StatePublished - 1 Mar 2019

Keywords

  • Calderón’s problem
  • Fractional schrödinger equation
  • Maximum principle
  • Nonlocal
  • Partial data
  • Semilinear

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