Inverse problems for elliptic equations with fractional power type nonlinearities

Tony Liimatainen, Yi Hsuan Lin*, Mikko Salo, Teemu Tyni

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not known. By using a fractional order adaptation of this method, we show that the results of [24,23] remain valid for general power type nonlinearities.

Original languageEnglish
Pages (from-to)189-219
Number of pages31
JournalJournal of Differential Equations
Volume306
DOIs
StatePublished - 5 Jan 2022

Keywords

  • Calderón problem
  • Higher order linearization
  • Inverse boundary value problem
  • Partial data
  • Semilinear elliptic equations
  • Transversally anisotropic manifold

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