Abstract
We prove operator-norm resolvent convergence estimates for one-dimensional periodic differential operators with rapidly oscillating coefficients in the non-uniformly elliptic high-contrast setting, which has been out of reach of the existing homogenisation techniques. Our asymptotic analysis is based on a special representation of the resolvent of the operator in terms of the M-matrix of an associated boundary triple (“Krein resolvent formula”). The resulting asymptotic behaviour is shown to be described, up to a unitary transformation, by a non-standard version of the Kronig–Penney model on \({\mathbb{R}}\).
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Communicated by P. Deift
To the memory of Professor Yuri Safarov
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Cherednichenko, K.D., Kiselev, A.V. Norm-Resolvent Convergence of One-Dimensional High-Contrast Periodic Problems to a Kronig–Penney Dipole-Type Model. Commun. Math. Phys. 349, 441–480 (2017). https://doi.org/10.1007/s00220-016-2698-4
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DOI: https://doi.org/10.1007/s00220-016-2698-4