Compactness and dichotomy in nonlocal shape optimization

Autores
Parini, E.; Salort, Ariel Martin
Año de publicación
2020
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under homogeneous Dirichlet boundary conditions. Exploiting a nonlocal version of Lions' concentration-compactness principle, we prove that either an optimal shape exists or there exists a minimizing sequence consisting of two “pieces” whose mutual distance tends to infinity. Our work is inspired by similar results obtained by Bucur in the local case.
Fil: Parini, E.. Aix Marseille Université; Francia
Fil: Salort, Ariel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
FRACTIONAL DIFFERENTIAL EQUATIONS
SHAPE OPTIMIZATION
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/143906
Acceder
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network_name_str CONICET Digital (CONICET)
spelling Compactness and dichotomy in nonlocal shape optimizationParini, E.Salort, Ariel MartinFRACTIONAL DIFFERENTIAL EQUATIONSSHAPE OPTIMIZATIONhttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under homogeneous Dirichlet boundary conditions. Exploiting a nonlocal version of Lions' concentration-compactness principle, we prove that either an optimal shape exists or there exists a minimizing sequence consisting of two “pieces” whose mutual distance tends to infinity. Our work is inspired by similar results obtained by Bucur in the local case.Fil: Parini, E.. Aix Marseille Université; FranciaFil: Salort, Ariel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaWiley VCH Verlag2020-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/143906Parini, E.; Salort, Ariel Martin; Compactness and dichotomy in nonlocal shape optimization; Wiley VCH Verlag; Mathematische Nachrichten; 293; 11; 11-2020; 2208-22320025-584XCONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1002/mana.201800234info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/10.1002/mana.201800234info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1806.01165info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:57:27Zoai:ri.conicet.gov.ar:11336/143906instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:57:27.809CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Compactness and dichotomy in nonlocal shape optimization
title Compactness and dichotomy in nonlocal shape optimization
spellingShingle Compactness and dichotomy in nonlocal shape optimization
Parini, E.
FRACTIONAL DIFFERENTIAL EQUATIONS
SHAPE OPTIMIZATION
title_short Compactness and dichotomy in nonlocal shape optimization
title_full Compactness and dichotomy in nonlocal shape optimization
title_fullStr Compactness and dichotomy in nonlocal shape optimization
title_full_unstemmed Compactness and dichotomy in nonlocal shape optimization
title_sort Compactness and dichotomy in nonlocal shape optimization
dc.creator.none.fl_str_mv Parini, E.
Salort, Ariel Martin
author Parini, E.
author_facet Parini, E.
Salort, Ariel Martin
author_role author
author2 Salort, Ariel Martin
author2_role author
dc.subject.none.fl_str_mv FRACTIONAL DIFFERENTIAL EQUATIONS
SHAPE OPTIMIZATION
topic FRACTIONAL DIFFERENTIAL EQUATIONS
SHAPE OPTIMIZATION
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under homogeneous Dirichlet boundary conditions. Exploiting a nonlocal version of Lions' concentration-compactness principle, we prove that either an optimal shape exists or there exists a minimizing sequence consisting of two “pieces” whose mutual distance tends to infinity. Our work is inspired by similar results obtained by Bucur in the local case.
Fil: Parini, E.. Aix Marseille Université; Francia
Fil: Salort, Ariel Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description We prove a general result about the behaviour of minimizing sequences for nonlocal shape functionals satisfying suitable structural assumptions. Typical examples include functions of the eigenvalues of the fractional Laplacian under homogeneous Dirichlet boundary conditions. Exploiting a nonlocal version of Lions' concentration-compactness principle, we prove that either an optimal shape exists or there exists a minimizing sequence consisting of two “pieces” whose mutual distance tends to infinity. Our work is inspired by similar results obtained by Bucur in the local case.
publishDate 2020
dc.date.none.fl_str_mv 2020-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/143906
Parini, E.; Salort, Ariel Martin; Compactness and dichotomy in nonlocal shape optimization; Wiley VCH Verlag; Mathematische Nachrichten; 293; 11; 11-2020; 2208-2232
0025-584X
CONICET Digital
CONICET
url http://hdl.handle.net/11336/143906
identifier_str_mv Parini, E.; Salort, Ariel Martin; Compactness and dichotomy in nonlocal shape optimization; Wiley VCH Verlag; Mathematische Nachrichten; 293; 11; 11-2020; 2208-2232
0025-584X
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1002/mana.201800234
info:eu-repo/semantics/altIdentifier/url/https://onlinelibrary.wiley.com/doi/10.1002/mana.201800234
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1806.01165
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Wiley VCH Verlag
publisher.none.fl_str_mv Wiley VCH Verlag
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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