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arXiv · 1510.03364

Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model

Kirill D. Cherednichenko·Alexander V. Kiselev
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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 equivalent transformation, by a non-standard version of the Kronig-Penney model on $\mathbb R$.

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Kirill D. Cherednichenko, Alexander V. Kiselev. 2015-10-12. Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model. https://doi.org/10.1007/s00220-016-2698-4

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