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Estimates for capacity and discrepancy of convex surfaces in sieve-like domains with an application to homogenization
Univ Edinburgh, Sch Math, Edinburgh, Midlothian, Scotland..
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
2016 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 55, no 6Article in journal (Refereed) Published
Abstract [en]

We consider the intersection of a convex surface Gamma with a periodic perforation of R-d, which looks like a sieve, given by T epsilon = boolean OR(d)(k is an element of Z) {epsilon k + a epsilon T} where T is a given compact set and a epsilon << epsilon is the size of the perforation in the epsilon-cell (0, epsilon)(d) subset of R-d. When epsilon tends to zero we establish uniform estimates for p- capacity, 1 < p < d, of the set Gamma n T-epsilon. Additionally, we prove that the intersections Gamma boolean AND {epsilon k + a(epsilon)T}(k) are uniformly distributed over Gamma and give estimates for the discrepancy of the distribution. As an application we show that the thin obstacle problem with the obstacle defined on the intersection of Gamma and the perforations, in a given bounded domain, is homogenizable when p < 1+ d/4. This result is new even for the classical Laplace operator.

Place, publisher, year, edition, pages
2016. Vol. 55, no 6
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-313544DOI: 10.1007/s00526-016-1088-2ISI: 000390043500009OAI: oai:DiVA.org:uu-313544DiVA: diva2:1070347
Available from: 2017-02-01 Created: 2017-01-20 Last updated: 2017-11-29Bibliographically approved

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