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On the Regularity of Non-scattering Anisotropic Inhomogeneities
Journal article   Open access   Peer reviewed

On the Regularity of Non-scattering Anisotropic Inhomogeneities

Fioralba Cakoni, Michael S. Vogelius and Jingni Xiao
Archive for rational mechanics and analysis, v 247(3), 31
01 Jun 2023
DOI: https://doi.org/10.1007/s00205-023-01863-y
Featured in Collection :   UN Sustainable Development Goals @ Drexel
url
https://arxiv.org/abs/2208.13231View
Submitted Open arXiv.org - Non-exclusive license to distribute

Abstract

Mathematics, Applied Science & Technology Mathematics Mechanics Physical Sciences Technology
In this paper we examine the necessary conditions for an anisotropic inhomogeneous medium to be non-scattering at a single wave number and for a single incident field. These conditions are expressed in terms of the regularity of the boundary of the inhomogeneity. We assume that the coefficients, characterizing the constitutive material properties of the medium, are sufficiently smooth, and that the incident wave is appropriately non-degenerate. Our analysis utilizes the Hodograph transform as well as regularity results for nonlinear elliptic partial differential equations. Our approach requires that the boundary a-priori is of class C-1,C-a for some 0 < a < 1.

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12 citations in Web of Science
5 citations in Scopus

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Collaboration types
Domestic collaboration
Web of Science research areas
Mathematics, Applied
Mechanics
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