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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 R.
- High-contrast homogenisation, boundary triples, Krein formula, norm-resolvent estimates, quantum graphs, asymptotic analysis
FingerprintDive into the research topics of 'Norm-resolvent convergence of one-dimensional high-contrast periodic problems to a Kronig-Penney dipole-type model'. Together they form a unique fingerprint.
- 1 Finished
23/07/14 → 22/06/19
Project: Research council