Homogenization of a Boundary Value Problem for the n-Laplace Operator on a n-Dimensional Domain with Rapidly Alternating Boundary Condition Type: The Critical Case
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We study the asymptotic behavior of the solution of a boundary value problem for the p-Laplace operator with rapidly alternating nonlinear boundary conditions posed on ε-periodically arranged subsets on the boundary of a domain Ω ⊂ ℝn. We assume that p = n, construct a homogenized problem, and prove the weak convergence as ε → 0 of the solution of the original problem to the solution of the homogenized problem in the so-called critical case, which is characterized by the fact that the homogenization changes the character of nonlinearity of the boundary condition.
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- 2.Gomez, D., Perez, M.E., Podolskii, A.V., and Shaposhnikova, T.A., Homogenization of variational in-equalities for the p-Laplace operator in perforated media along manifolds, Appl. Math. Optim., 2017, vol. 475, pp. 1–19.Google Scholar
- 5.Diaz, J.I., Gomez-Castro, D., Shaposhnikova, T.A., and Zubova, M.N., Change of homogenized absorption term in diffusion processes with reaction on the boundary of periodically distributed asymmetric particles of critical size, Electron. J. Differ. Equ., 2017, no. 178, pp. 1–25.Google Scholar
- 9.Diaz, J.I., Gomez-Castro, D., Podol’skii, A.V., and Shaposhnikova, T.A., Characterizing the strange term in critical size homogenization: quasilinear equations with a nonlinear boundary condition involving a general maximal monotone graph, Adv. Nonlinear Anal., 2017, doi: https://doi.org/10.1515/anona-2017-0140.
- 11.Diaz, J.I., Gomez-Castro, D., Podolskiy A.V., and Shaposhnikova, T.A., Homogenization of a net of periodic critically scaled boundary obstacles related to reverse osmosis “nano-composite” membranes, Adv. Nonlinear Anal., 2018, doi: https://doi.org/10.1515/anona-2018-0158.