{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T12:28:34Z","timestamp":1787228914394,"version":"build-2736575974"},"reference-count":20,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100004100","name":"Labex","doi-asserted-by":"publisher","award":["ANR-11-LABX-0056- LMH"],"award-info":[{"award-number":["ANR-11-LABX-0056- LMH"]}],"id":[{"id":"10.13039\/501100004100","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Multiscale Model. Simul."],"published-print":{"date-parts":[[2017,1]]},"abstract":"<jats:p>The aim of the paper is to introduce an alternative notion of two-scale convergence which gives a more natural modeling approach to the homogenization of partial differential equations with periodically oscillating coefficients: while removing the bother of the admissibility of test functions, it nevertheless simplifies the proof of all the standard compactness results which made classical two-scale convergence very worthy of interest. Bounded sequences in $L^2_{\\sharp} [ {Y}, L^2 (\\Omega) ]$ and $L^2_{\\sharp} [ {Y}, H^1 (\\Omega) ]$ are proven to be relatively compact with respect to this new type of convergence. The strengths of the notion are highlighted on the classical homogenization problem of linear second-order elliptic equations for which first-order boundary corrector-type results are also established. Eventually, possible weaknesses of the method are pointed out on a nonlinear problem: the weak two-scale compactness result for ${\\bf S}^2$-valued stationary harmonic maps.<\/jats:p>","DOI":"10.1137\/16m1085309","type":"journal-article","created":{"date-parts":[[2017,11,14]],"date-time":"2017-11-14T12:37:10Z","timestamp":1510663030000},"page":"1651-1671","source":"Crossref","is-referenced-by-count":1,"title":["Cell Averaging Two-Scale Convergence: Applications to Periodic Homogenization"],"prefix":"10.1137","volume":"15","author":[{"given":"Fran\u00e7ois","family":"Alouges","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giovanni","family":"Di Fratta","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,11,14]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/0523084"},{"key":"atypb2","unstructured":"G. Allaire,\n                      Shape Optimization by the Homogenization Method\n                      , Appl. Math. Sci. 146, Springer, New York, 2012."},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1051\/cocv:1999110"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2015.0365"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01161995"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1016\/S1631-073X(02)02429-9"},{"key":"atypb7","doi-asserted-by":"crossref","unstructured":"D. Cioranescu and P. Donato,\n                      An Introduction to Homogenization\n                      , Oxford Lecture Ser. Math. 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