2011/05/23 by Colin Guillarmou, Albin, Pierre, Guillarmou, Colin +3 · 1 citation
Mathematics · #35R30 #58J32 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems
paper · doi:10.48550/arxiv.1105.4565
openalex publication_date 2011/05/23 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We prove identification of coefficients up to gauge 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 bundle 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 determines 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.