2008/07/05 by Giovanni Alessandrini, Romina Gaburro · 36 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Boundary (topology) #Boundary value problem #Composite Material Mechanics #Dirichlet distribution #Geometry #Inverse #Mathematical analysis #Mathematics #Neumann boundary condition #Numerical methods in inverse problems #Omega #Physics #Pointwise #Pure mathematics #Uniqueness #math.AP #msc:35R30
paper · pdf · doi:10.1080/03605300903017397
published in Communications in Partial Differential Equations 34(8), 918-936 (Taylor & Francis) · 16 pages, submitted
arxiv created 2008/07/05 · openalex publication_date 2009/07/22 · arxiv updated 2012/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body Ω ⊂ ℝ n when the so-called Dirichlet-to-Neumann map is locally given on a non empty portion Γ of the boundary ∂Ω. We extend results of uniqueness and stability at the boundary, obtained by the same authors in SIAM J. Math. Anal. 33:153–171, where the Dirichlet-to-Neumann map was given on all of ∂Ω instead. We also obtain a pointwise stability result at the boundary among the class of conductivities which are continuous at some point y ∈ Γ. Our arguments also apply when the local Neumann-to-Dirichlet map is available.