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Slow convergence in periodic homogenization problems for divergence-type elliptic operators
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). University of Edinburgh, United Kingdom.ORCID iD: 0000-0003-4834-6476
2016 (English)In: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 48, no 5, p. 3345-3382Article in journal (Refereed) Published
Abstract [en]

We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence-type elliptic operators. The construction is applied in two settings. First, we show that solutions to boundary layer problems for divergence-type elliptic equations set in halfspaces and with in finitely smooth data may converge to their corresponding boundary layer tails as slowly as one wishes depending on the position of the hyperplane. Second, we construct a Dirichlet problem for divergence-type elliptic operators set in a bounded domain, and with all data being C-infinity-smooth, for which the boundary value homogenization holds with arbitrarily slow speed.

Place, publisher, year, edition, pages
Society for Industrial and Applied Mathematics, 2016. Vol. 48, no 5, p. 3345-3382
Keywords [en]
boundary layers, periodic homogenization, slow convergence, Dirichlet problem, ellipticity, halfspace, asymptotics, Diophantine direction, Gaussian curvature
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-199020DOI: 10.1137/15M1040165ISI: 000387324900010Scopus ID: 2-s2.0-84994173319OAI: oai:DiVA.org:kth-199020DiVA, id: diva2:1066761
Note

QC 20170119

Available from: 2017-01-19 Created: 2016-12-22 Last updated: 2017-11-29Bibliographically approved

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