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Abstract
We study the asymptotic behaviour of the resolvents \({(\mathcal{A}^\varepsilon+I)^{1}}\) of elliptic secondorder differential operators \({{\mathcal{A}}^\varepsilon}\) in \({\mathbb{R}^d}\) with periodic rapidly oscillating coefficients, as the period \({\varepsilon}\) goes to zero. The class of operators covered by our analysis includes both the “classical” case of uniformly elliptic families (where the ellipticity constant does not depend on \({\varepsilon}\)) and the “doubleporosity” case of coefficients that take contrasting values of order one and of order \({\varepsilon^2}\) in different parts of the period cell. We provide a construction for the leading order term of the “operator asymptotics” of \({(\mathcal{A}^\varepsilon+I)^{1}}\) in the sense of operatornorm convergence and prove order \({O(\varepsilon)}\) remainder estimates.
Original language  English 

Pages (fromto)  10611086 
Number of pages  26 
Journal  Archive for Rational Mechanics and Analysis 
Volume  219 
Issue number  3 
Early online date  7 Sept 2015 
DOIs  
Publication status  Published  1 Mar 2016 
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Dive into the research topics of 'Resolvent estimates for highcontrast elliptic problems with periodic coefficients'. 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