High-frequency stability estimates for the linearized inverse boundary value problem for the polyharmonic operator with constant attenuation

In this article, we explore high-frequency stability estimates for the determination of the zeroth-order perturbation of the polyharmonic operator with constant attenuation from the linearized partial Dirichlet-to-Neumann map when part of the boundary of the domain is inaccessible and flat. Our result suggests improvement of the stability when the frequency is appropriately chosen. This work extends the results of [17], [29], [19], [8] and [28] to the case of polyharmonic operator with constant attenuation and with lower regularity assumption on the potentials.

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Publication Details

Journal
Communications on Analysis and Computation
Published
2025-01-01
DOI
https://doi.org/10.3934/cac.2025010
Primary Topic
Numerical methods in inverse problems
Type
article
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article

High-frequency stability estimates for the linearized inverse boundary value problem for the polyharmonic operator with constant attenuation

Anupam Pal Choudhury, Ajith Kumar T
Communications on Analysis and Computation
Numerical methods in inverse problems
article

High-frequency stability estimates for the linearized inverse boundary value problem for the polyharmonic operator with constant attenuation

Anupam Pal Choudhury, Ajith Kumar T
article en

Abstract

In this article, we explore high-frequency stability estimates for the determination of the zeroth-order perturbation of the polyharmonic operator with constant attenuation from the linearized partial Dirichlet-to-Neumann map when part of the boundary of the domain is inaccessible and flat. Our result suggests improvement of the stability when the frequency is appropriately chosen. This work extends the results of [17], [29], [19], [8] and [28] to the case of polyharmonic operator with constant attenuation and with lower regularity assumption on the potentials.

Communications on Analysis and ComputationVol. 4(0)
National Institute of Science Education and Research (IN), Homi Bhabha National Institute (IN)
Openalex Percentile: Top 83%
Numerical methods in inverse problems
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