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Journal article
On the Regularity of Non-scattering Anisotropic Inhomogeneities
Archive for rational mechanics and analysis, v 247(3), 31
01 Jun 2023
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Abstract
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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Details
- Title
- On the Regularity of Non-scattering Anisotropic Inhomogeneities
- Creators
- Fioralba Cakoni - Rutgers, The State University of New JerseyMichael S. Vogelius - Rutgers State Univ, Dept Math, New Brunswick, NJ 08854 USAJingni Xiao - Drexel University, Mathematics
- Publication Details
- Archive for rational mechanics and analysis, v 247(3), 31
- Publisher
- Springer Nature
- Number of pages
- 15
- Grant note
- DMS-22-05912; DMS-21-06255 / NSF; National Science Foundation (NSF) FA9550-20-1-0024 / AFOSR; United States Department of Defense; Air Force Office of Scientific Research (AFOSR)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000964266500002
- Scopus ID
- 2-s2.0-85152537145
- Other Identifier
- 991021861280604721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Mechanics