Norm-Resolvent Convergence of One-Dimensional High-Contrast Periodic Problems to a Kronig-Penney Dipole-Type Model.

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 $${\mathbb{R}}$$ . [ABSTRACT FROM AUTHOR]