Partial data inverse problems for the Hodge Laplacian

Francis J. Chung, Mikko Salo, Leo Tzou

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


We prove uniqueness results for a Calderón-type inverse problem for the Hodge Laplacian acting on graded forms on certain manifolds in three dimensions. In particular, we show that partial measurements of the relative-to-absolute or absolute-to-relative boundary value maps uniquely determine a zeroth-order potential. The method is based on Carleman estimates for the Hodge Laplacian with relative or absolute boundary conditions, and on the construction of complex geometrical optics solutions which reduce the Calderón-type problem to a tomography problem for 2-tensors. The arguments in this paper allow us to establish partial data results for elliptic systems that generalize the scalar results due to Kenig, Sjöstrand and Uhlmann.

Original languageEnglish
Pages (from-to)43-93
Number of pages51
JournalAnalysis and PDE
Issue number1
StatePublished - 2017

Bibliographical note

Publisher Copyright:
© 2017 Mathematical Sciences Publishers.


  • Absolute and relative boundary conditions
  • Admissible manifolds
  • Carleman estimates
  • Hodge Laplacian
  • Inverse problems
  • Partial data

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Applied Mathematics


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