uu.seUppsala University Publications
Change search
ReferencesLink to record
Permanent link

Direct link
Highly oscillating thin obstacles
KTH, Matematik (Avd.).
2013 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 237, 286-315 p.Article in journal (Refereed) Published
Abstract [en]

The focus of this paper is on a thin obstacle problem where the obstacle is defined on the intersection between a hyper-plane Gamma in R-n and a periodic perforation T-epsilon of R-n, depending on a small parameters epsilon > 0. As epsilon -> 0, it is crucial to estimate the frequency of intersections and to determine this number locally. This is done using strong tools from uniform distribution. By employing classical estimates for the discrepancy of sequences of type {k alpha}(k=1)(infinity), alpha is an element of R, we are able to extract rather precise information about the set Gamma boolean AND T-epsilon. As epsilon -> 0, we determine the limit u of the solution u(epsilon) to the obstacle problem in the perforated domain, in terms of a limit equation it solves. We obtain the typical "strange term" behavior for the limit problem, but with a different constant taking into account the contribution of all different intersections, that we call the averaged capacity. Our result depends on the normal direction of the plane, but holds for a.e. normal on the unit sphere in R-n.

Place, publisher, year, edition, pages
2013. Vol. 237, 286-315 p.
Keyword [en]
Homogenization, Thin obstacle, Ergodicity, Discrepancy, Corrector
National Category
URN: urn:nbn:se:uu:diva-268042DOI: 10.1016/j.aim.2013.01.007ISI: 000316512500008ScopusID: 2-s2.0-84874437735OAI: oai:DiVA.org:uu-268042DiVA: diva2:875692
Available from: 2013-04-22 Created: 2015-12-01 Last updated: 2015-12-07Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopusFulltext, KTH

Search in DiVA

By author/editor
Strömqvist, Martin
In the same journal
Advances in Mathematics

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 43 hits
ReferencesLink to record
Permanent link

Direct link