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- Title
Norm-Resolvent Convergence of One-Dimensional High-Contrast Periodic Problems to a Kronig-Penney Dipole-Type Model.
- Authors
Cherednichenko, Kirill; Kiselev, Alexander
- 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 $${\mathbb{R}}$$ .
- Subjects
RESOLVENTS (Mathematics); STOCHASTIC convergence; KRONIG-Penney model; ESTIMATES; DIFFERENTIAL operators; ASYMPTOTIC homogenization
- Publication
Communications in Mathematical Physics, 2017, Vol 349, Issue 2, p441
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-016-2698-4