Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Gamma-convergence of stratified media with measure-valued limits
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-3125-3030
2000 (English)In: Asymptotic Analysis, ISSN 0921-7134, E-ISSN 1875-8576, Vol. 22, no 04-mar, 261-302 p.Article in journal (Refereed) Published
Abstract [en]

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).

Place, publisher, year, edition, pages
2000. Vol. 22, no 04-mar, 261-302 p.
Identifiers
URN: urn:nbn:se:kth:diva-19694ISI: 000086558600004OAI: oai:DiVA.org:kth-19694DiVA: diva2:338386
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2017-12-12Bibliographically approved

Open Access in DiVA

No full text

Authority records BETA

Gustafsson, Björn

Search in DiVA

By author/editor
Gustafsson, Björn
By organisation
Mathematics
In the same journal
Asymptotic Analysis

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 13 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf