Uniform asymptotics of Green's kernels in perforated domains and meso-scale approximations
2012 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, Vol. 57, no 2-4, 137-154 p.Article in journal (Refereed) Published
The article is a review of the authors' results on asymptotic approximations of Green's kernels for elliptic boundary value problems in perforated domains. A new feature is the uniformity of the asymptotics with respect to the independent variables. Formal asymptotic approximations are supplied with estimates of the remainder terms. For the case when the number of perforations or inclusions becomes large, a novel method of meso-scale asymptotic approximations is discussed, and uniform asymptotic approximations of Green's kernels as well as solutions of boundary value problems in multiply perforated domains are presented. Such approximations do not require periodicity or other typical constraints attributed to homogenization approximations.
Place, publisher, year, edition, pages
Taylor & Francis, 2012. Vol. 57, no 2-4, 137-154 p.
uniform asymptotic approximations, Green's functions, singularly perturbed domains
IdentifiersURN: urn:nbn:se:liu:diva-89713DOI: 10.1080/17476933.2011.581755OAI: oai:DiVA.org:liu-89713DiVA: diva2:609208
Complex and Real Analysis and Applications, in honour of Professor Robert P. Gilbert on the occasion of his 80th birthday2013-03-042013-03-042013-05-14