Publication
A nonlinear eigenvalue optimization problem: optimal potential functions
| dc.contributor.author | Antunes, Pedro R. S. | |
| dc.contributor.author | Mohammadi, Seyyed Abbas | |
| dc.contributor.author | Voss, Heinrich | |
| dc.date.accessioned | 2018-02-26T10:26:49Z | |
| dc.date.available | 2019-04-01T00:30:38Z | |
| dc.date.issued | 2018-04 | |
| dc.description.abstract | In this paper we study the following optimal shape design problem: Given an open connected set Ω⊂RN and a positive number A∈(0,|Ω|), find a measurable subset D⊂Ω with |D|=A such that the minimal eigenvalue of −div(ζ(λ,x)∇u)+αχDu=λu in Ω, u=0 on ∂Ω, is as small as possible. This sort of nonlinear eigenvalue problems arises in the study of some quantum dots taking into account an electron effective mass. We establish the existence of a solution and we determine some qualitative aspects of the optimal configurations. For instance, we can get a nearly optimal set which is an approximation of the minimizer in ultra-high contrast regime. A numerical algorithm is proposed to obtain an approximate description of the optimizer. | pt_PT |
| dc.description.sponsorship | The research of the first author was partially supported by FCT, Portugal, through the program “Investigador FCT” with reference IF/00177/2013 and the scientific project PTDC/MAT-CAL/4334/2014. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.doi | https://doi.org/10.1016/j.nonrwa.2017.09.003 | pt_PT |
| dc.identifier.issn | 1468-1218 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/7176 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Elsevier | pt_PT |
| dc.subject | Nonlinear eigenvalue problem | pt_PT |
| dc.subject | Shape optimization | pt_PT |
| dc.subject | Ultra-high contrast regime | pt_PT |
| dc.subject | Quantum dots | pt_PT |
| dc.title | A nonlinear eigenvalue optimization problem: optimal potential functions | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-CAL%2F4334%2F2014/PT | |
| oaire.citation.endPage | 327 | pt_PT |
| oaire.citation.startPage | 307 | pt_PT |
| oaire.citation.title | Nonlinear Analysis: Real World Applications | pt_PT |
| oaire.citation.volume | 40 | pt_PT |
| oaire.fundingStream | 3599-PPCDT | |
| person.familyName | Antunes | |
| person.givenName | Pedro | |
| person.identifier.ciencia-id | 6710-138C-A69D | |
| person.identifier.orcid | 0000-0003-1969-1860 | |
| person.identifier.rid | M-2406-2015 | |
| person.identifier.scopus-author-id | 55346859100 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | restrictedAccess | pt_PT |
| rcaap.type | article | pt_PT |
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