Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues

The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental frequency, are derived. The main question is whether or not the cla...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Bandle, Catherine, Wagner, Alfred
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.12.2015
Subjects
Eigenvalues
Inequalities
Resonant frequencies
Shape optimization
Transplantation
Online AccessGet full text

Cover

Abstract The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental frequency, are derived. The main question is whether or not the classical isoperimetric inequalities for the fundamental frequency of membranes hold in this case. The arguments are based on the harmonic transplantation for the global results and the shape derivatives (domain variations) for nearly circular domain.
AbstractList The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the largest negative eigenvalues, which have the same properties as the fundamental frequency, are derived. The main question is whether or not the classical isoperimetric inequalities for the fundamental frequency of membranes hold in this case. The arguments are based on the harmonic transplantation for the global results and the shape derivatives (domain variations) for nearly circular domain.
Author Bandle, Catherine
Wagner, Alfred
Author_xml – sequence: 1
  givenname: Catherine
  surname: Bandle
  fullname: Bandle, Catherine
– sequence: 2
  givenname: Alfred
  surname: Wagner
  fullname: Wagner, Alfred
BookMark eNqNjsEKgkAYhJcoyMp3WOgs6JrmPYrudZetfvWX9V_bXQ17-pboAToNM98MzIrNSRPMWCDSNImKnRBLFlrbxnEs8r3IsjRgt0sje-C6d9jhWzrUxCttuCQOSqGP7x6Ckc6HL3QNR6qQ0IGaeCdp4r226HAEP3lwglp-DWANNEo1gN2wRSWVhfCna7Y9Ha-Hc9Qb_fTcla0eDHlUirhIC5Hk_vB_rQ-1g0iY
ContentType Paper
Copyright 2015. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
Copyright_xml – notice: 2015. This work is published under http://arxiv.org/licenses/nonexclusive-distrib/1.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.
DBID 8FE
8FG
ABJCF
ABUWG
AFKRA
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
HCIFZ
L6V
M7S
PIMPY
PQEST
PQQKQ
PQUKI
PRINS
PTHSS
DatabaseName ProQuest SciTech Collection
ProQuest Technology Collection
Materials Science & Engineering Collection
ProQuest Central (Alumni)
ProQuest Central
ProQuest Central Essentials
ProQuest Central
Technology Collection
ProQuest One Community College
ProQuest Central
SciTech Premium Collection (Proquest) (PQ_SDU_P3)
ProQuest Engineering Collection
ProQuest Engineering Database
Publicly Available Content Database
ProQuest One Academic Eastern Edition (DO NOT USE)
ProQuest One Academic
ProQuest One Academic UKI Edition
ProQuest Central China
Engineering Collection
DatabaseTitle Publicly Available Content Database
Engineering Database
Technology Collection
ProQuest Central Essentials
ProQuest One Academic Eastern Edition
ProQuest Central (Alumni Edition)
SciTech Premium Collection
ProQuest One Community College
ProQuest Technology Collection
ProQuest SciTech Collection
ProQuest Central China
ProQuest Central
ProQuest Engineering Collection
ProQuest One Academic UKI Edition
ProQuest Central Korea
Materials Science & Engineering Collection
ProQuest One Academic
Engineering Collection
DatabaseTitleList Publicly Available Content Database
Database_xml – sequence: 1
  dbid: 8FG
  name: ProQuest Technology Collection
  url: https://search.proquest.com/technologycollection1
  sourceTypes: Aggregation Database
DeliveryMethod fulltext_linktorsrc
Discipline Physics
EISSN 2331-8422
Genre Working Paper/Pre-Print
GroupedDBID 8FE
8FG
ABJCF
ABUWG
AFKRA
ALMA_UNASSIGNED_HOLDINGS
AZQEC
BENPR
BGLVJ
CCPQU
DWQXO
FRJ
HCIFZ
L6V
M7S
M~E
PIMPY
PQEST
PQQKQ
PQUKI
PRINS
PTHSS
ID FETCH-proquest_journals_20838216233
IEDL.DBID BENPR
IngestDate Thu Oct 10 18:52:32 EDT 2024
IsOpenAccess true
IsPeerReviewed false
IsScholarly false
Language English
LinkModel DirectLink
MergedId FETCHMERGED-proquest_journals_20838216233
OpenAccessLink https://www.proquest.com/docview/2083821623?pq-origsite=%requestingapplication%
PQID 2083821623
PQPubID 2050157
ParticipantIDs proquest_journals_2083821623
PublicationCentury 2000
PublicationDate 20151215
PublicationDateYYYYMMDD 2015-12-15
PublicationDate_xml – month: 12
  year: 2015
  text: 20151215
  day: 15
PublicationDecade 2010
PublicationPlace Ithaca
PublicationPlace_xml – name: Ithaca
PublicationTitle arXiv.org
PublicationYear 2015
Publisher Cornell University Library, arXiv.org
Publisher_xml – name: Cornell University Library, arXiv.org
SSID ssj0002672553
Score 3.012199
SecondaryResourceType preprint
Snippet The paper deals with an eigenvalue problems possessing infinitely many positive and negative eigenvalues. Inequalities for the smallest positive and the...
SourceID proquest
SourceType Aggregation Database
SubjectTerms Eigenvalues
Inequalities
Resonant frequencies
Shape optimization
Transplantation
Title Shape optimization for an elliptic operator with infinitely many positive and negative eigenvalues
URI https://www.proquest.com/docview/2083821623
hasFullText 1
inHoldings 1
isFullTextHit
isPrint
link http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LSwMxEB7sLoI3n_ioJaDXQJN9mD0Jyq5FaCk-oLeSbLIq2N3arYIXf7uTmOpB6DEJCUlIZr6Z-TIBOM-yql8ynlLFuKaxqBSVvOQU0UHKZCZU5diEw1E6eIxvJ8nEO9xaT6tcyUQnqHVTWh85GukiEpyhtr6cv1H7a5SNrvovNDoQcrQU-gGEV_lofPfrZeHpBWLm6J-gddqj2IZwLOdmsQMbpt6FTUe6LNs9UPfPWE8avLUz_xySIIYksiY2TSZWl9hoXCCcWIcpwePwYkHi6yeZ4S0mP5SrD4NdNKnNk8viTYzNsGmzeJt2H86K_OF6QFcTm_rD007_lhodQFA3tTkEkjGpKs2UQZMmTnWSSfsavM-1FhGLDT-C7rqRjtc3n8AWIoHE8jRY0oVguXg3p6htl6oHHVHc9PzGYmn4lX8Dz76MIg
link.rule.ids 783,787,12777,21400,33385,33756,43612,43817
linkProvider ProQuest
linkToHtml http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LSwMxEB60RezNJz6qBvQaaLIPd08exHXVtghW6G1JNrMq2N3abQX_vZO41YPQa0JCEpKZLzPfzABcxHHRy4UMuRbScD8qNFcyl5zQQShUHOnCsQkHwzB99u_HwbgxuNUNrXIpE52gNlVubeT0SY-8SArS1lfTD26rRlnvalNCYx3avke62kaKJ7e_NhYZXhJi9v6JWac7ki1oP6opzrZhDcsd2HCUy7zeBf30Su2sojc7aYIhGSFIpkpmk2RSc06d6NzgzJpLGV2GNwsR37_YhN4w-yFcfSINMazEF5fDm6HNr2lzeGO9B-fJzeg65cuFZc3VqbO_jXr70CqrEg-AxULpwgiN9KHxQxPEysaC96QxkSd8lIfQXTXT0eruM9hMR4N-1r8bPhxDhzBBYBkbIuhCaz5b4Anp3bk-dYf7DZoCi5Y
openUrl ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Shape+optimization+for+an+elliptic+operator+with+infinitely+many+positive+and+negative+eigenvalues&rft.jtitle=arXiv.org&rft.au=Bandle%2C+Catherine&rft.au=Wagner%2C+Alfred&rft.date=2015-12-15&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422