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Uniform asymptotics of Green's kernels in perforated domains and meso-scale approximations
University of Liverpool, Liverpool, UK.
Department of Mathematical Sciences, University of Liverpool, UK.
2012 (English)In: Complex Variables and Elliptic Equations, ISSN 1747-6933, E-ISSN 1747-6941, Vol. 57, no 2-4, 137-154 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
uniform asymptotic approximations, Green's functions, singularly perturbed domains
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-89713DOI: 10.1080/17476933.2011.581755OAI: oai:DiVA.org:liu-89713DiVA: diva2:609208
Note

Special Issue:

Complex and Real Analysis and Applications, in honour of Professor Robert P. Gilbert on the occasion of his 80th birthday

Available from: 2013-03-04 Created: 2013-03-04 Last updated: 2017-12-06

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Maz´ya, Vladimir

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