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Asymptotic Behaviour of Cuboids Optimising Laplacian EigenvaluesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2017 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 89, no 4, p. 607-629Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Springer Basel , 2017. Vol. 89, no 4, p. 607-629
##### Keywords [en]

Asymptotics, Cuboids, Eigenvalues, Laplacian, Spectral optimisation
##### National Category

Mathematical Analysis
##### Identifiers

URN: urn:nbn:se:kth:diva-227117DOI: 10.1007/s00020-017-2407-5ISI: 000416537600008Scopus ID: 2-s2.0-85032668674OAI: oai:DiVA.org:kth-227117DiVA, id: diva2:1204560
#####

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##### Funder

Swedish Research Council
##### Note

##### In thesis

We prove that in dimension n≥ 2 , within the collection of unit-measure cuboids in Rn (i.e. domains of the form ∏i=1n(0,an)), any sequence of minimising domains RkD for the Dirichlet eigenvalues λk converges to the unit cube as k→ ∞. Correspondingly we also prove that any sequence of maximising domains RkN for the Neumann eigenvalues μk within the same collection of domains converges to the unit cube as k→ ∞. For n= 2 this result was obtained by Antunes and Freitas in the case of Dirichlet eigenvalues and van den Berg, Bucur and Gittins for the Neumann eigenvalues. The Dirichlet case for n= 3 was recently treated by van den Berg and Gittins. In addition we obtain stability results for the optimal eigenvalues as k→ ∞. We also obtain corresponding shape optimisation results for the Riesz means of eigenvalues in the same collection of cuboids. For the Dirichlet case this allows us to address the shape optimisation of the average of the first k eigenvalues.

QC 20180508

Available from: 2018-05-08 Created: 2018-05-08 Last updated: 2019-10-18Bibliographically approved1. Asymptotic and universal spectral estimates with applications in many-body quantum mechanics and spectral shape optimization$(function(){PrimeFaces.cw("OverlayPanel","overlay1313048",{id:"formSmash:j_idt1181:0:j_idt1185",widgetVar:"overlay1313048",target:"formSmash:j_idt1181:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

doi
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