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Slow convergence in periodic homogenization problems for divergence-type elliptic operators
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematik (Avd.). University of Edinburgh, United Kingdom.ORCID-id: 0000-0003-4834-6476
2016 (engelsk)Inngår i: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 48, nr 5, s. 3345-3382Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
Society for Industrial and Applied Mathematics, 2016. Vol. 48, nr 5, s. 3345-3382
Emneord [en]
boundary layers, periodic homogenization, slow convergence, Dirichlet problem, ellipticity, halfspace, asymptotics, Diophantine direction, Gaussian curvature
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Identifikatorer
URN: urn:nbn:se:kth:diva-199020DOI: 10.1137/15M1040165ISI: 000387324900010Scopus ID: 2-s2.0-84994173319OAI: oai:DiVA.org:kth-199020DiVA, id: diva2:1066761
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QC 20170119

Tilgjengelig fra: 2017-01-19 Laget: 2016-12-22 Sist oppdatert: 2017-11-29bibliografisk kontrollert

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