TY - JOUR
T1 - On the Regularity of Non-scattering Anisotropic Inhomogeneities
AU - Cakoni, Fioralba
AU - Vogelius, Michael S.
AU - Xiao, Jingni
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH, DE, part of Springer Nature.
PY - 2023/6
Y1 - 2023/6
N2 - 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 C1,α for some 0 < α< 1.
AB - 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 C1,α for some 0 < α< 1.
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U2 - 10.1007/s00205-023-01863-y
DO - 10.1007/s00205-023-01863-y
M3 - Article
AN - SCOPUS:85152537145
SN - 0003-9527
VL - 247
JO - Archive For Rational Mechanics And Analysis
JF - Archive For Rational Mechanics And Analysis
IS - 3
M1 - 31
ER -