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Abstract
We prove operatornorm resolvent convergence estimates for onedimensional periodic differential operators with rapidly oscillating coefficients in the nonuniformly elliptic highcontrast 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 Mmatrix of an associated boundary triple (“Krein resolvent formula”). The resulting asymptotic behaviour is shown to be described, up to a unitary transformation, by a nonstandard version of the Kronig–Penney model on R.
Original language  English 

Pages (fromto)  441480 
Number of pages  40 
Journal  Communications in Mathematical Physics 
Volume  349 
Issue number  2 
Early online date  25 Jul 2016 
DOIs  
Publication status  Published  1 Jan 2017 
Keywords
 Highcontrast homogenisation, boundary triples, Krein formula, normresolvent estimates, quantum graphs, asymptotic analysis
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Dive into the research topics of 'Normresolvent convergence of onedimensional highcontrast periodic problems to a KronigPenney dipoletype model'. Together they form a unique fingerprint.Projects
 1 Finished

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council