Inverse problems with partial data for elliptic operators on unbounded Lipschitz domains

Jussi Behrndt, Jonathan Rohleder*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For a second order formally symmetric elliptic differential expression we show that the knowledge of the Dirichlet-to-Neumann map or Robin-to-Dirichlet map for suitably many energies on an arbitrarily small open subset of the boundary determines the self-adjoint operator with a Dirichlet boundary condition or with a (possibly non-self-adjoint) Robin boundary condition uniquely up to unitary equivalence. These results hold for general Lipschitz domains, which can be unbounded and may have a non-compact boundary, and under weak regularity assumptions on the coefficients of the differential expression.

Original languageEnglish
Article number035009
JournalInverse problems
Volume36
Issue number3
DOIs
Publication statusPublished - 1 Jan 2020

Keywords

  • Calderon problem
  • Dirichlet-to-Neumann map
  • elliptic differential operator
  • Gelfand problem
  • inverse problem

ASJC Scopus subject areas

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

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