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.
KeywordsDiffusion Equation Linear Elasticity Macroscopic Quantity Reasonable Boundary Condition Classical Representation Theorem
Unable to display preview. Download preview PDF.
- 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