Abstract
In this note we consider the homogenization problem for a matrix locally periodic elliptic operator on Rd of the form A ε = −divA(x, x/ε)∇. The function A is assumed to be Hölder continuous with exponent s ∈ [0, 1] in the “slow” variable and bounded in the “fast” variable. We construct approximations for (A ε − μ)−1, including one with a corrector, and for (−Δ)s/2(A ε − μ)−1 in the operator norm on L 2(Rd)n. For s ≠ 0, we also give estimates of the rates of approximation.
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N. N. Senik, https://arxiv.org/abs/1703.02023.
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Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 51, No. 2, pp. 92–96, 2017 Original Russian Text Copyright © by N. N. Senik
Research supported by Young Russian Mathematics award and RFBR grant 16-01-00087.
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Senik, N.N. On homogenization for non-self-adjoint locally periodic elliptic operators. Funct Anal Its Appl 51, 152–156 (2017). https://doi.org/10.1007/s10688-017-0178-z
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DOI: https://doi.org/10.1007/s10688-017-0178-z