INVERSE PROBLEMS FOR THE FRACTIONAL LAPLACE EQUATION WITH LOWER ORDER NONLINEAR PERTURBATIONS

Ru Yu Lai, Laurel Ohm

Research output: Contribution to journalArticlepeer-review

Abstract

We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings.

Original languageEnglish (US)
Pages (from-to)305-323
Number of pages19
JournalInverse Problems and Imaging
Volume16
Issue number2
DOIs
StatePublished - Feb 2022
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgment. R.-Y. Lai was partially supported by NSF grant DMS-1714490 and DMS-2006731. L. Ohm was supported by NSF grant DMS-1714490 during summer 2020 and NSF grant DMS-2001959.

Publisher Copyright:
© 2022, American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Fractional Laplacian
  • Inverse problems
  • Nonlinear perturbations

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