Homogenisation and \(\theta-2\) convergence. (English) Zbl 0886.35017

Summary: We introduce a new concept of convergence for bounded sequences of functions in \(L^2(\Omega)\), called \(\theta-2\) convergence, where \(\Omega\) is an open set of \(\mathbb{R}^n\) and \(\theta\) a \(C^2\) diffeomorphism of \(\mathbb{R}^n\). This tool enables us to deal with homogenisation problems in some nonperiodic perforated domains. In particular, it provides a simple proof, and extensions, of a recent result of M. Briane [J. Math. Pures Appl. 73, No. 1, 47-66 (1994; Zbl 0835.35016)].


35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)


Zbl 0835.35016
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