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Applications of Fourier analysis in homogenization of Dirichlet problem I. Pointwise estimates
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). The University of Edinburgh.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).ORCID-id: 0000-0002-1316-7913
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
2013 (engelsk)Inngår i: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 254, nr 6, s. 2626-2637Artikkel i tidsskrift (Fagfellevurdert) 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.

##### sted, utgiver, år, opplag, sider
2013. Vol. 254, nr 6, s. 2626-2637
##### Emneord [en]
Elliptic systems, Homogenization, Oscillatory integrals
##### Identifikatorer
ISI: 000315240300011Scopus ID: 2-s2.0-84873120263OAI: oai:DiVA.org:kth-119722DiVA, id: diva2:612774
##### Forskningsfinansiär
Swedish Research Council

QC 20130325

Tilgjengelig fra: 2013-03-25 Laget: 2013-03-21 Sist oppdatert: 2017-06-20bibliografisk kontrollert

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Aleksanyan, HaykShahgholian, HenrikSjölin, Per
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Journal of Differential Equations

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