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NTIS 바로가기Journal of the Korean Society for Industrial and Applied Mathematics, v.27 no.2, 2023년, pp.87 - 108
SHOTA FUKUSHIMA (DEPARTMENT OF MATHEMATICS AND INSTITUTE OF APPLIED MATHEMATICS, INHA UNIVERSITY) , YONG-GWAN JI (SCHOOL OF MATHEMATICS, KOREA INSTITUTE FOR ADVANCED STUDY) , HYEONBAE KANG (DEPARTMENT OF MATHEMATICS AND INSTITUTE OF APPLIED MATHEMATICS, INHA UNIVERSITY) , YOSHIHISA MIYANISHI (DEPARTMENT OF MATHEMATICAL SCIENCES, FACULTY OF SCIENCE, SHINSHU UNIVERSITY)
This is a review paper on recent development on the spectral theory of the Neumann-Poincaré operator. The topics to be covered are convergence rate of eigenvalues of the Neumann-Poincaré operator and surface localization of the single layer potentials of its eigenfunctions. Study on th...
K. Ando, H. Kang, Y. Miyanishi and M. Putinar, Spectral analysis of Neumann-Poincare operator, Rev.?Roumaine Math. Pures Appl, Vol. LXVI (2021), 545-575.
D. Khavinson, M. Putinar and H.S. Shapiro, Poincare's variational problem in potential theory ' , Arch. Rational?Mech. Anal, 185 (2007), 143-184.
S. Fukushima, H. Kang and Y. Miyanishi, Decay rate of the eigenvalues of the Neumann-Poincare operator,?arXiv:2304.04772.
K. Ando and H. Kang, Analysis of plasmon resonance on smooth domains using spectral properties of the?Neumann-Poincare operator, Jour. Math. Anal. Appl, 435 (2016), 162-178.
H. Ammari, G. Ciraolo, H. Kang, H. Lee and G.W. Milton, Spectral theory of a Neumann-Poincare-type?operator and analysis of cloaking due to anomalous localized resonance, Arch. Rational Mech. Anal, 208?(2013), 667-692.
R. C. McPhedran and G. W. Milton, A review of anomalous resonance, its associated cloaking, and superlensing, C. R. Phy, 21 (2020), 409-423.
H. Ammari and H. Kang, Polarization and moment tensors with applications to inverse problems and effective?medium theory, Applied Mathematical Sciences, Vol. 162, Springer-Verlag, New York, 2007.
K. Ando, H. Kang and Y. Miyanishi, Exponential decay estimates of the eigenvalues for the Neumann-Poincare operator on analytic boundaries in two dimensions, J. Integr. Equ. Appl, 30 (2018), 473-489.
E. Bonnetier and H. Zhang, Characterization of the essential spectrum of the Neumann-Poincare operator in?2D domains with corner via Weyl sequences, Rev. Mat. Iberoam, 35 (2019), 925-948.
J. Helsing and K.-M. Perfekt, On the Polarizability and Capacitance of the Cube, Applied and Computational?Harmonic Analysis, 34 (2013), 445-468.
J. Helsing and K.-M. Perfekt, The spectra of harmonic layer potential operators on domains with rotationally?symmetric conical points, J. Math. Pures Appl, 118 (2018), 235--287.
H. Kang, M. Lim and S. Yu, Spectral resolution of the Neumann-Poincare operator on intersecting disks and?analysis of plasmon resonance, Arch. Rational Mech. Anal, 226(1) (2017), 83-115.
K.-M. Perfekt and M. Putinar, Spectral bounds for the Neumann-Poincare operator on planar domains with?corners, J. d'Analyse Math, 124 (2014), 39-57.
K.M. Perfekt and M. Putinar, The essential spectrum of the Neumann-Poincare operator on a domain with?corners, Arch. Rational Mech. Anal, 223 (2017), 1019-1033.
K.-M. Perfekt. Plasmonic eigenvalue problem for corners: limiting absorption principle and absolute continuity in the essential spectrum, J. Math. Pures Appl, 145 (2021), 130-162.
Y. Miyanishi, Weyl's law for the eigenvalues of the Neumann-Poincare operators in three dimensions: Will-more energy and surface geometry, Adv. Math, 406 (2022), 108547.
Y. Miyanishi and G. Rozenblum, Eigenvalues of the Neumann-Poincare operator in dimension 3: Weyl's law?and geometry, Algebra i Analiz 31(2) (2019), 248-268; reprinted in St. Petersburg Math. J, 31(2) (2020),?371-386.
Y. Jung and M. Lim, A decay estimate for the eigenvalues of the Neumann-Poincare operator using the Grunsky coefficients, Proc. Amer. Math. Soc, 148 (2020), 591-600.
Y. Miyanishi and T. Suzuki, Eigenvalues and eigenfunctions of double layer potentials, Trans. Amer. Math.?Soc. 369 (2017), 8037-8059.
J. Delgado and M. Ruzhansky, Schatten classes on compact manifolds: kernel conditions, J. Funct. Anal,?267(3) (2014), 772-798.
S. Fukushima and H. Kang, Spectral structure of the Neumann-Poincare operator on axially symmetric functions, in preparation.
K. Ando, H. Kang, Y. Miyanishi and T. Nakazawa, Surface localization of plasmons in three dimensions and?convexity, SIAM J. Appl. Math, 81 (2021), 1020-1033.
Y. Ji and H. Kang, A concavity condition for existence of a negative value in Neumann-Poincare spectrum in?three dimensions, Proc. Amer. Math. Soc, 147 (2019), 3431-3438.
M. S. Birman and M. Z. Solomjak, Asymptotic behavior of the spectrum of pseudodifferential operators?with anisotropically homogeneous symbols, Vestnik Leningrad. Univ, (13 Mat. Meh. Astronom. vyp. 3), 169?(1977), 13-21.
G.W. Milton and N.-A.P. Nicorovici, On the cloaking effects associated with anomalous localized resonance,?Proc. R. Soc. A, 462 (2006), 3027-3059.
D. Chung, H. Kang, K. Kim and H. Lee, Cloaking due to anomalous localized resonance in plasmonic structures of confocal ellipses, SIAM J. Appl. Math, 74 (2014), 1691-1707.
H. Ammari, G. Ciraolo, H. Kang, H. Lee and G.W. Milton, Spectral theory of a Neumann-Poincare-type?operator and analysis of anomalous localized resonance II, Contemporary Math, 615 (2014), 1-14.
H. Ammari, H. Kang, and H. Lee, A boundary integral method for computing elastic moment tensors for?ellipses and ellipsoids, J. Comp. Math, 25 (1) (2007), 2-12.
V.D. Kupradze, Potential methods in the theory of elasticity, Daniel Davey & Co., New York, 1965.
K. Ando, Y. Ji, H. Kang, K. Kim and S. Yu, Spectral properties of the Neumann-Poincare operator and?cloaking by anomalous localized resonance for the elasto-static system, Euro. J. Appl. Math, 29 (2018), 189-225.
B.E.J. Dahlberg, C.E. Kenig and G.C. Verchota, Boundary value problems for the systems of elastostatics in?Lipschitz domains, Duke Math. J, 57(3) (1988), 795-818.
S. Fukushima, Y.-G. Ji, and H. Kang, A decomposition theorem of surface vector fields and spectral structure?of the Neumann-Poincare operator in elasticity, arXiv:2211.15879.
N.I. Muskhelishvili, Singular integral equations. Boundary problems of function theory and their application?to mathematical physics, Translated from the second (1946) Russian edition and with a preface by J. R. M.?Radok, Noordhoff International Publishing-Leyden, 1977.
A.P. Calderon, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sc. USA, 74?(1977), 1324-1327.
L. Escauriaza, E. B. Fabes, and G. Verchota, On a regularity theorem for weak solutions to transmission?problems with internal Lipchitz boundaries, Proc. Amer. Math. Soc. 115 (4) (1992), 1069-1076.
G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz?domains, J. Funct. Anal, 59(3) (1984), 572-611.
K. Ando, H. Kang and Y. Miyanishi, Elastic Neumann-Poincare operators on three dimensional smooth?domains: Polynomial compactness and spectral structure, Int. Math. Res. Notices, 12 (2019), 3883-3900.
K. Ando, H. Kang and Y. Miyanishi, Convergence rate for eigenvalues of the elastic Neumann-Poincare?operator on smooth and real analytic boundaries in two dimensions, Jour. Math. Pures Appl, 140 (2020),?211-229.
G. Rozenblum, The Discrete Spectrum of the Neumann-poincare Operator in 3D Elasticity, J. Pseudo-Differ.?Oper. Appl. 14 (2023), article number 26. https://doi.org/10.1007/s11868-023-00520-y.
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