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Applications of Fourier Analysis in Homogenization of Dirichlet Problem III: Polygonal Domains
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). The University of Edinburgh.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-1316-7913
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
2014 (English)In: Journal of Fourier Analysis and Applications, ISSN 1069-5869, E-ISSN 1531-5851, Vol. 20, no 3, 524-546 p.Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
Springer, 2014. Vol. 20, no 3, 524-546 p.
Keyword [en]
Homogenization, Dirichlet problem, Polygonal domain, Fourier analysis
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-148326DOI: 10.1007/s00041-014-9327-4ISI: 000337789300004Scopus ID: 2-s2.0-84902381152OAI: oai:DiVA.org:kth-148326DiVA: diva2:736329
Funder
Swedish Research Council
Note

QC 20140806

Available from: 2014-08-06 Created: 2014-08-05 Last updated: 2017-06-20Bibliographically approved

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Shahgholian, Henrik

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