Stable determination of an elastic medium scatterer by a single far-field measurement and beyond

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Original languageEnglish
Article number170
Journal / PublicationCalculus of Variations and Partial Differential Equations
Volume61
Issue number5
Online published24 Jun 2022
Publication statusPublished - Oct 2022

Abstract

We are concerned with the time-harmonic elastic scattering due to an inhomogeneous elastic material inclusion located inside a uniformly homogeneous isotropic medium. We establish a sharp stability estimate of logarithmic type in determining the support of the elastic scatterer, independent of its material content, by a single far-field measurement when the support is a convex polyhedral domain in Rn, = 2 , 3. Our argument in establishing the stability result is localized around a corner of the medium scatterer. This enables us to further establish a byproduct result by proving that if a generic medium scatterer, not necessary to be a polyhedral shape, possesses a corner, then there exists a positive lower bound of the scattered far-field patterns. The latter result indicates that if an elastic material object possesses a corner on its support, then it scatters every incident wave stably and invisibility phenomenon does not occur.