References
- Bakhvalov NS, Panasenko GP. Homogenization: averaging processes in periodic media. In: Mathematical problems in mechanics of composite materials. Vol. 36, Mathematics and its Applications (Soviet Series). Dordrecht: Kluwer Academic; 1989.
- Bensoussan A, Lions J-L, Papanicolaou G. Asymptotic analysis for periodic structures. Vol. 5, Studies in applied mathematics. Amsterdam: North-Holland; 1978.
- Zhikov VV, Kozlov SM, Olejnik OA. Homogenization of differential operators. Berlin: Springer-Verlag; 1994.
- Birman MSh, Suslina TA. Second order periodic differential operators. Threshold properties and homogenization. Algebra i Analiz. 2003;15:1–108. English transl., St. Petersburg Math. J. 2004;15(5):639--714.
- Birman MSh, Suslina TA. Homogenization with corrector term for periodic elliptic differential operators. Algebra i Analiz. 2005;17:1–104. English transl., St. Petersburg Math. J. 2006;17(6):897--973.
- Birman MSh, Suslina TA. Homogenization with corrector term for periodic differential operators. Approximation of solutions in the Sobolev class H1(ℝd). Algebra i Analiz. 2006;18:1–130. English transl., St. Petersburg Math. J. 2007;18(6):857--955.
- Suslina TA. Homogenization of periodic second order differential operators including first order terms. In: Birman MS, Uraltseva NN, editor. Spectral theory of differential operators. Vol. 225, American Mathematical Society Translation Seriers 2. Providence (RI): American Mathematical Society; 2008. p. 227–252.
- Suslina TA. Homogenization in the Sobolev class H1(ℝd) for second order periodic elliptic operators with the inclusion of first order terms. Algebra i Analiz. 2010;22:108–222. English transl., St. Petersburg Math. J. 2011;22(1):81--162.
- Suslina TA. Homogenization of elliptic systems with periodic coefficients: operator error estimates in L2(ℝd) with corrector taken into account. Algebra i Analiz. 2014;26:195–263. English transl., St. Petersburg Math. J. 2015;26(4):643--693.
- Zhikov VV. On the operator estimates in the homogenization theory. Dokl. Ros. Akad. Nauk. 2005;403:305–308. English transl., Dokl. Math. 2005;72:535--538.
- Zhikov VV, Pastukhova SE. On operator estimates for some problems in homogenization theory. Russ. J. Math. Phys. 2005;12:515–524.
- Griso G. Error estimate and unfolding for periodic homogenization. Asymptot. Anal. 2004;40:269–286.
- Griso G. Interior error estimate for periodic homogenization. Anal. Appl. 2006;4:61–79.
- Kenig CE, Lin F, Shen Z. Convergence rates in L2 for elliptic homogenization problems. Arch. Ration. Mech. Anal. 2012;203:1009–1036.
- Pakhnin MA, Suslina TA. Operator error estimates for homogenization of the elliptic Dirichlet problem in a bounded domain. Algebra i Analiz. 2012;24:139–177. English transl., St. Petersburg Math. J. 2013;24(6):949--976.
- Suslina TA. Homogenization of the Dirichlet problem for elliptic systems: L2-operator error estimates. Mathematika. 2013;59:463–476.
- Suslina TA. Homogenization of the Neumann problem for elliptic systems with periodic coefficients. SIAM J. Math. Anal. 2013;45:3453–3493.
- Suslina TA. Homogenization of elliptic problems depending on a spectral parameter. Funktsional. Anal. i Prilozhen. 2014;48:88–94. English transl., Funct. Anal. Appl.2014;48(4):299--303.
- Suslina TA. Homogenization of elliptic operators with periodic coefficients in dependence of the spectral parameter. Algebra i Analiz. 2015;27:87–166. English transl., St. Petersburg Math. J. 2016;27(4):to appear. Preprint available from: http://arxiv.org/abs/1406.7530.
- Borisov DI. Asymptotics for the solutions of elliptic systems with rapidly oscillating coefficients. Algebra i Analiz. 2008;20:19–42. English transl., St. Petersburg Math.J. 2009;20(2):175--191.
- Meshkova YuM, Suslina TA. Homogenization of solutions of initial boundary value problems for parabolic systems. Funktsional. Anal. i Prilozhen. 2015;49:88–93. English transl., Funct. Anal. Appl. 2015;49(1):72--76.
- Meshkova YuM, Suslina TA. Homogenization of initial boundary value problems for parabolic systems with periodic coefficients. Appl. Anal. Forthcoming. Published on-line, Available from: http://www.tandfonline.com/doi/full/10.1080/00036811.2015.1068300#abstract.
- Meshkova YuM, Suslina TA. Homogenization of solutions of the boundary-value problems for elliptic systems with rapidly oscillating coefficients. In preparation.
- Ladyzhenskaya OA, Uralt’seva NN. Linear and quasilinear elliptic equations. Vol. 46, Mathematics in science and engineering. New York (NY): Academic Press; 1968.