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Gamma-convergence of stratified media with measure-valued limitsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2000 (English)In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576, Vol. 22, no 04-mar, p. 261-302Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

2000. Vol. 22, no 04-mar, p. 261-302
##### Identifiers

URN: urn:nbn:se:kth:diva-19694ISI: 000086558600004OAI: oai:DiVA.org:kth-19694DiVA, id: diva2:338386
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt721",{id:"formSmash:j_idt721",widgetVar:"widget_formSmash_j_idt721",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt727",{id:"formSmash:j_idt727",widgetVar:"widget_formSmash_j_idt727",multiple:true});
#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt748",{id:"formSmash:j_idt748",widgetVar:"widget_formSmash_j_idt748",multiple:true});
##### Note

QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

We consider energy functionals, or Dirichlet forms, [GRAPHICS] for a class G of bounded domains Omega subset of R-N, with epsilon>0 a fine structure parameter and with symmetric conductivity matrices A(epsilon) = (a(ij)(epsilon)) is an element of L-loc(infinity)(R)(NxN) which are functions only of the first coordinate x(1) and which are locally uniformly elliptic for each fixed epsilon>0. We show that if the functions (of x(1)) b(11)(epsilon) = 1/a(11)(epsilon), b(1j)(epsilon) = a(1j)(epsilon)/a(11)(epsilon) (j greater than or equal to 2), b(ij)(epsilon) = a(ij)(epsilon) - a(i1)(epsilon)a(1j)(epsilon)/ a(11)(epsilon) (i, j greater than or equal to 2) converge weakly* as measures towards corresponding limit measures b(ij) as epsilon --> 0, if the (1,1)-coefficient m(11)(epsilon) of (A(epsilon))(-1) is bounded in L-loc(1)(R) and if none of its weak* cluster measures has atoms in common with b(ii), i greater than or equal to 2, then the family J(epsilon) = {J(Omega)(epsilon)}(Omega is an element of g) Gamma-converges in a local sense towards a naturally defined limit family J = {J(Omega))(Omega is an element of G) as epsilon-->0. An alternative way of formulating the conclusion is to say that the energy densities (A(epsilon)del u,del u) Gamma-converge in a distributional sense towards the corresponding limit density. Writing J(Omega)(epsilon) in terms of B-epsilon = (b(ij)(epsilon)) it becomes [GRAPHICS] and the definition of J(Omega) and the limit density (A del u, del u) is obtained by properly replacing the b(ij)(epsilon) is an element of L-loc(infinity)(R) by the limit measures b(ij) and making sense to everything for u in a certain linear subspace of L-loc(2)(R-N).

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