Local data inverse problem for the polyharmonic operator with anisotropic perturbations

2023/07/20 by Sombuddha Bhattacharyya, Bhattacharyya, Sombuddha, Pranav Kumar +1 · 1 citation
Computer Science · Mathematics · #31B20 #31B30 #35J40 #35R30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2307.10608

openalex publication_date 2023/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study an inverse problem with local data for a linear polyharmonic operator with several lower order tensorial perturbations. We consider our domain to have an inaccessible portion of the boundary where neither the input can be prescribed nor the output can be measured. We prove the unique determination of all the tensorial coefficients of the operator from the knowledge of the Dirichlet and Neumann map on the accessible part of the boundary, under suitable geometric assumptions on the domain.

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