Inverse Boundary Problems for Systems in Two Dimensions

Pierre Albin, Colin Guillarmou, Leo Tzou, Gunther Uhlmann

Research output: Contribution to journalArticlepeer-review


We prove identification of coefficients up to gauge equivalence by Cauchy data at the boundary for elliptic systems on oriented compact surfaces with boundary or domains of ℂ. In the geometric setting, we fix a Riemann surface with boundary and consider both a Dirac-type operator plus potential acting on sections of a Clifford module and a connection Laplacian plus potential (i.e. Schrödinger Laplacian with external Yang-Mills field) acting on sections of a Hermitian bundle. In either case we show that the Cauchy data determine both the connection and the potential up to a natural gauge transformation: conjugation by an endomorphism of the bundle which is the identity at the boundary. For domains of ℂ, we recover zeroth order terms up to gauge from Cauchy data at the boundary in first order elliptic systems.

Original languageEnglish (US)
Pages (from-to)1551-1571
Number of pages21
JournalAnnales Henri Poincare
Issue number6
StatePublished - Sep 2013

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics


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