Applications of Fourier Analysis in Homogenization of Dirichlet Problem III: Polygonal Domains
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
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
2014. Vol. 20, no 3, 524-546 p.
Homogenization, Dirichlet problem, Polygonal domain, Fourier analysis
IdentifiersURN: urn:nbn:se:kth:diva-148326DOI: 10.1007/s00041-014-9327-4ISI: 000337789300004ScopusID: 2-s2.0-84902381152OAI: oai:DiVA.org:kth-148326DiVA: diva2:736329
FunderSwedish Research Council
QC 201408062014-08-062014-08-052014-08-06Bibliographically approved