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Applications of Fourier analysis in homogenization of Dirichlet problem I. Pointwise estimates
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0002-1316-7913
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2013 (English)In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 254, no 6, 2626-2637 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we prove convergence results for homogenization problem for solutions of partial differential system with rapidly oscillating Dirichlet data. Our method is based on analysis of oscillatory integrals. In the uniformly convex and smooth domain, and smooth operator and boundary data, we prove pointwise convergence results, namely vertical bar u(epsilon)(x) - u(0)(x)vertical bar <= C-kappa epsilon((d-1)/2) 1/d(x)(kappa), for all x is an element of D, for all kappa > d - 1, where u(epsilon) and u(0) are solutions of respectively oscillating and homogenized Dirichlet problems, and d(x) is the distance of x from the boundary of D. As a corollary for all 1 <= p < infinity we obtain L-P convergence rate as well.

Place, publisher, year, edition, pages
2013. Vol. 254, no 6, 2626-2637 p.
Keyword [en]
Elliptic systems, Homogenization, Oscillatory integrals
National Category
URN: urn:nbn:se:kth:diva-119722DOI: 10.1016/j.jde.2012.12.017ISI: 000315240300011ScopusID: 2-s2.0-84873120263OAI: diva2:612774
Swedish Research Council

QC 20130325

Available from: 2013-03-25 Created: 2013-03-21 Last updated: 2013-03-25Bibliographically approved

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Shahgholian, HenrikSjölin, Per
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