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Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 5
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Research Article

Operator estimates for non-periodically perforated domains: disappearance of cavities

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Pages 859-873 | Received 23 Oct 2022, Accepted 21 Apr 2023, Published online: 04 May 2023

References

  • Díaz JI, Gómez-Castro D, Shaposhnikova TA. Nonlinear reaction–diffusion processes for nanocomposites: anomalous improved homogenization. Berlin: De Gruyter; 2021.
  • Jikov VV, Kozlov SM, Oleinik OA. Homogenization of differential operators. Moscow: Fiziko-Matematicheskaya Literatura; 1993. (in Russian).
  • Marchenko VA, Khruslov EY. Boundary value problems in domains with a fine-grained boundary. Naukova Dumka: Kiev; 1974. (in Russian).
  • Marchenko VA, Khruslov EY. Homogenization of partial differential equations. Boston: Birkhäuser; 2006.
  • Oleinik OA, Iosifyan GA, Shamaev AS. Mathematical problems in elasticity and homogenization. Amsterdam: North-Holland; 1992.
  • Gómez D, Lobo M, Pérez E, et al. Unilateral problems for the p-Laplace operator in perforated media involving large parameters. ESAIM Control Optim Calc Var 2018;24(3):921–964.
  • Kaizu S. The Poisson equation with semilinear boundary conditions in domains with many tiny holes. J Fac Sci Univ Tokyo Sect I A Math. 1989;36(1):43–86.
  • Kaizu S. The Poisson equation with nonautonomous semilinear boundary conditions in domains with many time holes. SIAM J Math Anal. 1991;22(5):1222–1245.
  • Khrabustovskyi A, Plum M. Operator estimates for homogenization of the Robin Laplacian in a perforated domain. J Differ Equ. 2022;338:474–517.
  • Khrabustovskyi A, Post O. Operator estimates for the crushed ice problem. Asymp Anal. 2018;110(3–4):137–161.
  • Pastukhova SE. Resolvent approximations in L2-norm for elliptic operators acting in a perforated space. Contem Math Fund Direct. 2020;66(2):314–334. (in Russian).
  • Suslina TA. Spectral approach to homogenization of elliptic operators in a perforated space. Rev Math Phys. 2018;30(08):Article ID 1840016.
  • Zhikov VV. Spectral method in homogenization theory. Proc Steklov Inst Math. 2005;250:85–94.
  • Cherednichenko K, Dondl P, Rösler F. Norm-resolvent convergence in perforated domains. Asymp Anal. 2018;110(3–4):163–184.
  • Anné C, Post O. Wildly perturbed manifolds: norm resolvent and spectral convergence. J Spectr Theory. 2021;11(1):229–279.
  • Borisov DI, Mukhametrakhimova AI. Uniform convergence and asymptotics for problems in domains finely perforated along a prescribed manifold in the case of the homogenized Dirichlet condition. Sb Math. 2021;212(8):1068–1121.
  • Borisov DI, Mukhametrakhimova AI. Norm convergence for problems with perforation along a given manifold with nonlinear Robin condition on boundaries of cavities; 2022. Preprint: arXiv:2202.10767; accepted for publication in St.-Petersburg Math. J.
  • Borisov D, Cardone G, Durante T. Homogenization and uniform resolvent convergence for elliptic operators in a strip perforated along a curve. Proc Roy Soc Edinburgh Sec A Math. 2016;146(6):1115–1158.
  • Borisov DI, Kříž J. Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: vanishing limit. Anal Math Phys. 2023;13(1):5.
  • Borisov D. Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: strange term; 2022. Preprint: arXiv:2205.09490.
  • Oleinik OA, Shaposhnikova TA. On homogenization of the Poisson equation in partially perforated domains with density of cavities and mixed type conditions on their boundary. Atti Accad Naz Lincei Cl Sci Fis Mat Natur Rend Lincei Mat Appl. 1996;7(3):129–146.
  • Dubinskii YA. Nonlinear elliptic and parabolic equations. J Math Sci. 1979;12(5):475–554.
  • Vainberg MM. Variational method and method of monotone operators in the theory of nonlinear equations. New York-Toronto: A Halsted Press Book; Jerusalem-London: John Wiley & Sons; 1973.
  • Griso G. Interior error estimate for periodic homogenization. Anal Appl. 2006;4(1):61–79.
  • Pastukhova SE. Homogenization estimates for singularly perturbed operators. J Math Sci. 2020;251(5):724–747.
  • Senik NN. Homogenization for non-self-adjoint periodic elliptic operators on an infinite cylinder. SIAM J Math Anal. 2017;49(2):874–898.
  • Suslina TA. Homogenization of the Neumann problem for elliptic systems with periodic coefficients. SIAM J Math Anal. 2013;45(6):3453–3493.
  • Suslina TA. Homogenization of the Dirichlet problem for elliptic systems: L2-operator error estimates. Mathematika. 2013;59(2):463–476.
  • Borisov DI. On operator estimates for planar domains with non-regular curving of boundary: Dirichlet and Neumann condition. J Math Sci. 2022;264(5):562–580.

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