Optimal stability estimate in the inverse boundary value problem for\n periodic potentials with partial data

2017/11/27 by Sombuddha Bhattacharyya, Bhattacharyya, Sombuddha, Cătălin I. Cârstea +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1711.09770

openalex publication_date 2017/11/27 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider the inverse boundary value problem for operators of the form\n- triangle+q in an infinite domain\n\Ω=\ℝ\×\ω\⊂\ℝ¹⁺ⁿ, n\≥3, with a\nperiodic potential q. For Dirichlet-to-Neumann data localized on a portion of\nthe boundary of the form \Γ₁=\ℝ\×\γ₁, with \γ₁\nbeing the complement either of a flat or spherical portion of \∂\ω,\nwe prove that a log-type stability estimate holds.\n

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