Remarks on Homogenization
Homogenization is concerned with the relations between microscopic and macroscopic scales but different mathematical problems can be associated to this general question: one of them is to give a probabilistic framework where microscopic quantitites are functions depending on a parameter ω lying in a probability space and macroscopic quantities are expectations of them [this may be the subject of another workshop], another one is to consider asymptotic expansions where one considers functions u(x,x/ε), where u(x,y) is periodic in y, which are called microscopic values, the macroscopic quantities being obtained by averaging in y.
KeywordsCoherence Convolution Dition Topo Milton
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- The missing details for III are contained in F. Murat-L. Tartar: Calcul des variations et homogénéisation, Collection de la Direction des Etudes et Recherches d’Electricité de France 57, Eyrolles, Paris 1985, which is contained in the lecture notes of a summer school on homogenization which, with the lectures of D. Bergman, J.L. Lions, G. Papanicolaou and E. Sanchez Palencia, gives a good overview of the field.Google Scholar
- The missing details for II are contained in L. Tartar: Estimations fines de coefficients homogénéisés, to appear in Research Notes in Mathematics Pitman 1985 (Collogue De Giorgi, P. Kree ed.) I referred in the text to many speakers at this workshop and thus to their written contributions to this volume that will certainly contain more complete bibliographical references.Google Scholar