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Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 13
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Articles

On resolvent approximations of elliptic differential operators with periodic coefficients

Pages 4453-4474 | Received 14 Feb 2020, Accepted 24 Nov 2020, Published online: 17 Dec 2020

References

  • Bensoussan A, Lions J-L, Papanicolaou G. Asymptotic analysis for periodic structures. Amsterdam: North Holland; 1978.
  • Sanchez-Palencia E. Non-homogeneous media and vibration theory. Berlin: Springer; 1980.
  • Bakhvalov NS, Panasenko G. Homogenisation: averaging processes in periodic media. Moscow: Nauka; 1984. (in Russian). Dordrecht: Kluwer Academic; 1989. (in English).
  • Jikov VV, Kozlov SM, Oleinik OA. Homogenization of differential operators and integral functionals. Berlin: Springer; 1994.
  • Birman MS, Suslina TA. Second order periodic differential operators. Threshold properties and homogenization. St. Petersburg Math J. 2004;15:639–714.
  • Zhikov VV. On operator estimates in homogenization theory. Dokl Math. 2005;72:535–538.
  • Zhikov VV. Spectral method in homogenization theory. Proc Steklov Inst Math. 2005;250:85–94.
  • Birman MS, Suslina TA. Homogenization with corrector term for periodic elliptic differential operators. St. Petersbg Math J. 2006;17:897–973.
  • Zhikov VV, Pastukhova SE. On operator estimates for some problems in homogenization theory. Russian J Math Phys. 2005;12:515–524.
  • Zhikov VV, Pastukhova SE. Estimates of homogenization for a parabolic equation with periodic coefficients. Russian J Math Phys. 2006;13:224–237.
  • Zhikov VV. Some estimates from homogenization theory. Dokl Math. 2006;73:96–99.
  • Pastukhova SE. Some estimates from homogenized elasticity problems. Dokl Math. 2006;73:102–106.
  • Cardone G, Pastukhova SE, Zhikov VV. Some estimates for nonlinear homogenization. Rend Accad Naz Sci XL Mem Mat Appl. 2005;29:101–110.
  • Zhikov VV, Pastukhova SE, Tikhomirova SV. On the homogenization of degenerate elliptic equations. Dokl Math. 2006;74:716–720.
  • Zhikov VV, Pastukhova SE. Homogenization of degenerate elliptic equations. Sib Math J. 2008;49:80–101.
  • Pastukhova SE, Tikhomirov RN. Operator estimates in reiterated and locally periodic homogenization. Dokl Math. 2007;76:548–553.
  • Pastukhova SE. Operator estimates in nonlinear problems of reiterated homogenization. Proc Steklov Inst Math. 2008;261:214–228.
  • Pastukhova SE. Estimates in homogenization of parabolic equations with locally periodic coefficients. Asymptot Anal. 2010;66:207–228.
  • Pastukhova SE. Approximation of the exponential of a diffusion operator with multiscale coefficients. Funct Anal Appl. 2014;48(3):183–197.
  • Zhikov VV, Pastukhova SE. Homogenization estimates of operator type for an elliptic equation with quasiperiodic coefficients. Russian J Math Phys. 2015;22(4):264–278.
  • Pastukhova SE. Operator error estimates for homogenization of fourth order elliptic equations. St. Petersburg Math J. 2017;28:273–289.
  • Pastukhova SE. Estimates in homogenization of higher-order elliptic operators. Appl Anal. 2019;5:1449–1466.
  • Zhikov VV, Pastukhova SE. Operator estimates in homogenization theory. Russian Math Surveys. 2016;71:417–511.
  • Pastukhova SE. Operator estimates in homogenization of elliptic systems of equations. J Math Sci. 2017;226(4):445–461.
  • Pastukhova SE, Tikhomirov RN. Operator-type estimates in homogenization of elliptic equations with lower order terms. St. Petersbg Math J. 2018;29:841–861.
  • Zhikov VV, Kozlov SM, Oleinik OA, et al. Averaging and G-convergence of differential operators. Russian Math Surveys. 1979;34(5):69–147.
  • Pastukhova SE. L2-estimates for homogenization of elliptic operators. J Math Sci. 2020;244(4):671–685.
  • Senik NN. Homogenization for non-self-adjoint periodic elliptic operators on an infinite cylinder. SIAM J Math Anal. 2017;49(9):874–898.
  • Pastukhova SE. Resolvent approximations in L2-norm for elliptic operators acting in a perforated space. Contemp Math Fund Direct. 2020;66(2):314–334.
  • Pastukhova SE. On resolvent approximations of elliptic differential operators with locally periodic coefficients. Lobachevskii J Math. 2020;41(5):814–834.
  • Pastukhova SE. Homogenization estimates for singularly perturbed operators. J Math Sci. 2020;251(5):724–747.
  • Pastukhova SE. Resolvent L2-approximation in homogenization of fourth order elliptic operators. Sbornik: Math. 2021;212(1):1–24.
  • Pastukhova SE. Resolvents in homogenization of higher order elliptic operators. J Math Sci. 2020;251(6):902–925.
  • Maz'ya VG, Verbitsky IE. Form boundedness of the general second-order differential operator. Comm Pure Appl Math. 2006;59(9):1286–1329.
  • Coifman R, Lions PL, Meyer Y, et al. Compensated compactness and Hardy spaces. J Math Pures Appl. 1993;72(3):247–286.
  • Stein EM. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. NJ: Princeton Univ. Press; 1993.
  • Seregin G, Silvestre L, Sverak V, et al. On divergence-free drifts. J Differ Equ. 2012;252:505–540.
  • Zhikov VV. Remarks on the uniqueness of a solution of the Dirichlet problem for second-order elliptic equations with lower-order terms. Funct Anal Appl. 2004;38(3):173–183.
  • Surnachev MD. On the uniqueness of solutions to stationary convection-diffusion equations with generalized divergence-free drift. Complex Var Elliptic Equ. 2018;68:1168–1184.
  • Pastukhova SE. Approximations of the resolvent for a non-self-adjoint diffusion operator with rapidly oscillating coefficients. Math Notes. 2013;94:127–145.
  • Pastukhova SE. Approximations of the operator exponential in a periodic diffusion problem with drift. Sb Math. 2013;204(2):280–306.

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