Reconstruction of singular and degenerate inclusions in Calderón's problem

Henrik Garde*, Nuutti Hyvönen

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Abstract

We consider the reconstruction of the support of an unknown perturbation to a known conductivity coefficient in Calderón's problem. In a previous result by the authors on monotonicity-based reconstruction, the perturbed coefficient is allowed to simultaneously take the values $0$ and $\infty$ in some parts of the domain and values bounded away from $0$ and $\infty$ elsewhere. We generalise this result by allowing the unknown coefficient to be the restriction of an $A_2$-Muckenhoupt weight in parts of the domain, thereby including singular and degenerate behaviour in the governing equation. In particular, the coefficient may tend to $0$ and $\infty$ in a controlled manner, which goes beyond the standard setting of Calderón's problem. Our main result constructively characterises the outer shape of the support of such a general perturbation, based on a local Neumann-to-Dirichlet map defined on an open subset of the domain boundary.
Original languageEnglish
JournalInverse Problems and Imaging
Volume16
Issue5
Pages (from-to)1219-1227
Number of pages9
ISSN1930-8337
DOIs
Publication statusPublished - Aug 2022

Keywords

  • Calderón's problem
  • electrical impedance tomography
  • monotonicity method
  • degenerate elliptic problem
  • singular elliptic problem
  • Calderon's problem
  • inclusion detection
  • SHAPE-RECONSTRUCTION

Cite this