References
- Bakhvalov NS , Panasenko GP . Homogenization: averaging processes in periodic media. Mathematical problems in mechanics of composite materials. Vol. 36, Mathematics and its Applications (Soviet Series). Dordrecht: Kluwer Acadamic Publishers Group; 1989.
- Bensoussan A , Lions J-L , Papanicolaou G . Asymptotic analysis for periodic structures. Vol. 5, Studies in Mathematics and its Applications. 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 Anal. 2003;15(5):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 Anal. 2005;17(6):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 Anal. 2006;18(6):1–130; English transl., St Petersburg Math J. 2007;18(6):857--955.
- Suslina TA . Homogenization of elliptic operators with periodic coefficients in dependence of the spectral parameter. Algebra Anal. 2015;27(4):87–166; English transl., St Petersburg Math J. 2016;27(4):651--708.
- Suslina TA . On homogenization of periodic parabolic systems. Funktsional Anal Prilozhen. 2004;38(4):86–90; English transl., Funct Anal Appl. 2004;38(4):309--312.
- Suslina TA . Homogenization of a periodic parabolic Cauchy problem. Amer Math Soc Transl. (2). 2007;220:201–233.
- Suslina TA . Homogenization of a periodic parabolic Cauchy problem in the Sobolev space H1 (ℝd). Math Model Nat Phenom. 2010;5(4):390–447.
- Vasilevskaya ES . A periodic parabolic Cauchy problem: homogenization with corrector. Algebra Anal. 2009;21(1):3–60; English transl., St Petersburg Math J. 2010;21(1):1--41.
- Vasilevskaya ES , Suslina TA . Homogenization of parabolic and elliptic periodic operators in L2 (ℝd) with the first and second correctors taken into account. Algebra Anal. 2012;24(2):1–103; English transl., St Petersburg Math J. 2013;24(2):185--261.
- Zhikov VV . On the operator estimates in the homogenization theory. Dokl Ros Akad Nauk. 2005;403(3):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(4):515–524.
- Zhikov VV , Pastukhova SE . Estimates of homogenization for a parabolic equation with periodic coefficients. Russ J Math Phys. 2006;13(2):224–237.
- Zhikov VV , Pastukhova SE . Operator estimates in homogenization theory. Uspekhi Matem Nauk. 2016;71(429)(3):27–122; English transl., Russian Math Surveys. 2016;71(3):417--511.
- Veniaminov NA . Homogenization of periodic differential operators of high order. Algebra Anal. 2010;22(5):69–103; English transl., St Petersburg Math J. 2011;22(5):751--775.
- Kukushkin AA , Suslina TA . Homogenization of high order elliptic operators with periodic coefficients. Algebra Anal. 2016;28(1):89–149; English transl., St Petersburg Math J. 2017;28(1):65--108.
- Pastukhova SE . Operator estimates for homogenization of fourth order elliptic equations. Algebra Anal. 2016;28(2):204–226; English transl., St Petersburg Math J. 2017;28(2).
- Pastukhova SE . Estimates in homogenization of higher-order elliptic operators. Appl Anal. 2016;16(2):1–18.
- Griso G . Error estimate and unfolding for periodic homogenization. Asymptot Anal. 2004;40(3–4):269–286.
- Griso G . Interior error estimate for periodic homogenization. Anal Appl. 2006;4(1):61–79.
- Pakhnin MA , Suslina TA . Operator error estimates for homogenization of the elliptic Dirichlet problem in a bounded domain. Algebra Anal. 2012;24(6):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(2):463–476.
- Suslina TA . Homogenization of the Neumann problem for elliptic systems with periodic coefficients. SIAM J Math Anal. 2013;45(6):3453–3493.
- Kenig CE , Lin F , Shen Z . Convergence rates in L2 for elliptic homogenization problems. Arch Ration Mech Anal. 2012;203:1009–1036.
- Meshkova YuM , Suslina TA . Homogenization of initial boundary value problems for parabolic systems with periodic coefficients. Appl Anal. 2016;95(8):1736–1775.
- Geng J , Shen Z . Convergence rates in parabolic homogenization with time-dependent periodic coefficients. J Funct Anal. 2017;272(5):2092–2113.
- Suslina TA . Homogenization of the Dirichlet problem for higher-order elliptic equations with periodic coefficients. Algebra Anal. 2017;29(2):139–192; English transl., St Petersburg Math J. 2018;29(2).
- Suslina TA . Homogenization of the Neumann problem for higher order elliptic equations with periodic coefficients. Complex Var Elliptic Equ. 30 Aug 2017. DOI:10.1080/17476933.2017.1365845
- Solonnikov VA . On general boundary value problems for elliptic systems in the sense of Douglis and Nirenberg. II. Proc Steklov Inst Math. 1968;92:269–339.
- Kondrat’ev VA , Eidelman SD . About conditions on boundary surface in the theory of elliptic boundary value problems. Dokl AN SSSR. 1979;246(4):812–815; English transl., Soviet Math Dokl. 1979;20:561--563.
- Mazya VG , Shaposhnikova TO . Theory of multipliers in spaces of differentiable functions. Vol. 23, Monographs and Studies in Mathematics. Brookling (NY): Pitman Publishing Co.; 1985.
- Stein EM . Singular integrals and differentiability properties of functions. Princeton (NJ): Princeton University Press; 1970.
- Kato T . Perturbation theory for linear operators. New York (NY): Springer-Verlag; 1966.
- Nečas J . Direct methods in the theory of elliptic equations. Springer Monographs in Mathematics. New York: Springer; 2012.