A uniqueness result in the inverse problem for the anisotropic Schrödinger type equation from local measurements

2025/05/23 by Donlon, Niall, Gaburro, Romina
#35J10 #35J25 #35R30 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.18063

Abstract

We consider the inverse boundary value problem of the simultaneous determination of the coefficients σ and q of the equation -div(σ∇ u)+qu = 0 from knowledge of the so-called Neumann-to-Dirichlet map, given locally on a non-empty curved portion Σ of the boundary ∂ Ω of a domain Ω⊂ ℝⁿ, with n≥ 3. We assume that σ and q are a-priori known to be a piecewise constant matrix-valued and scalar function, respectively, on a given partition of Ω with curved interfaces. We prove that σ and q can be uniquely determined in Ω from the knowledge of the local map.

Citations

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Related

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• Determining an anisotropic conductivity by boundary measurements: stability at the boundary
• Global Uniqueness for a Two-Dimensional Inverse Boundary Value Problem
• Inverse Boundary Value Problem by Partial data for the Neumann-to-Dirichlet-map in two dimensions