References
- Kamotski IV , Smyshlyaev VP . Two-scale homogenization for a class of partially degenerating PDE systems; 2013, arXiv:1309.4579v1. Available from: https://arxiv.org/abs/1309.4579v1
- Zhikov VV . On an extension and an application of the two-scale convergence method. Sbornik Math. 2000;191:973–1014.
- Zhikov VV . On spectrum gaps of some divergent elliptic operators with periodic coefficients. St Petersburg Math J. 2005; 16:773--790. Original publication: Algebra Anal. 2004;16:34--58.
- Zhikov VV , Pastukhova SE . On the Trotter-Kato theorem in a variable space. Funct Anal Appl. 2007;41:264–270.
- Zhikov VV , Pastukhova SE . On gaps in the spectrum of the operator of elasticity theory on a high contrast periodic structure. J Math Sci (N Y). 2013;188:227–240.
- Fenchenko VN , Khruslov EYa . Asymptotic behaviour or the solutions of differential equations with strongly oscillating and degenerating coefficient matrix. Dokl Akad Nauk Ukrain SSR Ser A. 1980;4:26–30.
- Arbogast T , Douglas J , Hornung U . Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J Math Anal. 1990;21:823–836.
- Auriault J-L , Bonnet G . Dynamique des composites elastiques periodiques. Arch Mech [Archiwum Mechaniki Stosowanej]. 1985;37:269–284.
- Khruslov EYa . Homogenized models of composite media. In: Dal Maso G , Dell’ Antonio GF , editors. Composite media and homogenization theory. Basel: Birkhäuser; 1991. p. 159–182.
- Panasenko GP . Multicomponent homogenization of processes in strongly nonhomogeneous structures. Math USSR Sbornik. 1991;69:143–153.
- Allaire G . Homogenization and two-scale convergence. SIAM J Math Anal. 1992;23:1482–1518.
- Sandrakov GV . Homogenization of elasticity equations with contrasting coefficients. Sbornik Math. 1999;190:1749–1806.
- Bouchitté G , Felbacq D . Homogenization near resonances and artificial magnetism from dielectrics. C R Math Acad Sci Paris. 2004;339:377–382.
- Cherednichenko KD , Smyshlyaev VP , Zhikov VV . Non-local homogenized limits for composite media with highly anisotropic periodic fibres. Proc Royal Soc Edinb A. 2006;136A:87–114.
- Babych NO , Kamotski IV , Smyshlyaev VP . Homogenization in periodic media with doubly high contrasts. Netw Heterog Media. 2008;3:413–436.
- Kohn RV , Shipman SP . Magnetism and homogenization of microresonators. Multiscale Model Simul. 2008;7:62–92.
- Ávila A , Griso G , Miara B , et al . Multiscale modeling of elastic waves: theoretical justification and numerical simulation of band gaps. Multiscale Model Simul. 2008;7:1–21.
- Cherdantsev M . Spectral convergence for high-contrast elliptic periodic problems with a defect via homogenization. Mathematika. 2009;55:29–57.
- Smyshlyaev VP . Propagation and localization of elastic waves in highly anisotropic periodic composites via two-scale homogenization. Mech Mater. 2009;41:434–447.
- Bellieud M . Torsion effects in elastic composites with high contrast. SIAM J Math Anal. 2010;41:2514–2553.
- Cooper S . Two-scale homogenisation of partially degenerating PDEs with applications to photonic crystals and elasticity [PhD thesis]. Bath; 2012.
- Chen Y , Lipton R . Resonance and double negative behavior in metamaterials. Arch Ration Mech Anal. 2013;209:835–868.
- Cooper S . Homogenisation and spectral convergence of a periodic elastic composite with weakly compressible inclusions. Appl Anal. 2014;93:1401–1430.
- Cooper S , Kamotski I , Smyshlyaev V . On band gaps in photonic crystal fibers; 2014, arXiv:1411.0238. Available from: https://arxiv.org/pdf/1411.0238.pdf
- Cherednichenko K , Cooper S . Homogenization of the system of high-contrast Maxwell equations. Mathematika. 2015;61:475–500.
- Bouchitté G , Bourel C , Felbacq D . Homogenization near resonances and artificial magnetism in three dimensional dielectric metamaterials. Arch Ration Mech Anal. 2017;225:1233–1277.
- Auriault J-L . Acoustics of heterogeneous media: macroscopic behavior by homogenization. Curr Top Acoust Res. 1994;1:63–90.
- Camar-Eddine M , Seppecher P . Determination of the closure of the set of elasticity functionals. Arch Ration Mech Anal. 2003;170:211–245.
- Milton GW , Briane M , Willis JR . On cloaking for elasticity and physical equations with a transformation invariant form. New J Phys. 2006;8:248 (1--20 pages).
- Pastukhova SE . On the convergence of hyperbolic semigroups in variable Hilbert spaces. J Math Sci (N Y). 2005;127:2263–2283.
- Nguetseng G . A general convergence result for a functional related to the theory of homogenization. SIAM J Math Anal. 1989;20:608–623.
- Fonseca I , Müller S . A-quasiconvexity, lower semicontinuity, and young measures. SIAM J Math Anal. 1999;30:1355–1390.
- Evans LC . Partial differential equations. Vol. 19, Graduate studies in mathematics. Providence (RI): American Mathematical Society; 2000.
- Jikov VV , Kozlov SM , Oleinik OA . Homogenization of differential operators and integral functionals. Berlin: Springer-Verlag; 1994.
- Briane M , Francfort GA . Loss of ellipticity through homogenization in linear elasticity. Math Models Methods Appl Sci. 2015;25:905–928.
- Chechkin GA , Piatnitski AL , Shamaev AS . Homogenization. Methods and applications. Vol. 234, Translations of mathematical monographs. Providence (RI): American Mathematical Society; 2007.
- Tartar L . An introduction to Sobolev spaces and interpolation spaces. Heidelberg: Springer; 2007.
- Lions JL , Magenes E . Nonhomogeneous boundary value problems and applications. Vol. I--III. Berlin, Heidelberg: Springer; 1972.
- Stein EM . Singular integrals and differentiability properties of functions. Princeton (NJ): Princeton University Press; 1970.