Recovering a quasilinear conductivity from boundary measurements

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Abstract

We consider the Calderón type inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open subset of small gradients, hence extending a partial result of Muñoz and Uhlmann to all real analytic conductivities. We also recover non-analytic conductivities with additional growth assumptions along large gradients. Moreover, the results hold for non-homogeneous conductivities if the non-homogeneous part is assumed known.

Original languageEnglish (US)
Article number015014
JournalInverse Problems
Volume37
Issue number1
DOIs
StatePublished - Dec 24 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Signal Processing
  • Mathematical Physics
  • Computer Science Applications
  • Applied Mathematics

Keywords

  • Calderon problem
  • conductivity
  • Dirichlet-to-Neumann map
  • elliptic
  • linearization
  • nonlinear
  • quasilinear

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