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Applications of Fourier Analysis in Homogenization of Dirichlet Problem III: Polygonal Domains
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). The University of Edinburgh.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.).ORCID-id: 0000-0002-1316-7913
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.).
2014 (engelsk)Inngår i: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 20, nr 3, s. 524-546Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

In this paper we prove convergence results for the homogenization of the Dirichlet problem for elliptic equations in divergence form with rapidly oscillating boundary data and non oscillating coefficients in convex polygonal domains. Our analysis is based on integral representation of solutions. Under a certain Diophantine condition on the boundary of the domain and smooth coefficients we prove pointwise, as well as convergence results. For larger exponents we prove that the convergence rate is close to optimal. We also suggest several directions of possible generalization of the results in this paper.

sted, utgiver, år, opplag, sider
Springer, 2014. Vol. 20, nr 3, s. 524-546
Emneord [en]
Homogenization, Dirichlet problem, Polygonal domain, Fourier analysis
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-148326DOI: 10.1007/s00041-014-9327-4ISI: 000337789300004Scopus ID: 2-s2.0-84902381152OAI: oai:DiVA.org:kth-148326DiVA, id: diva2:736329
Forskningsfinansiär
Swedish Research Council
Merknad

QC 20140806

Tilgjengelig fra: 2014-08-06 Laget: 2014-08-05 Sist oppdatert: 2017-06-20bibliografisk kontrollert

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