Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media

We consider here a nonlocal phase transition energy in a periodic medium and we construct solutions whose interfaces lie at a bounded distance from any given hyperplane. These solutions are either periodic or quasiperiodic, depending on the rational dependency of the normal direction to the referenc...

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Detalles Bibliográficos
Autores: Cozzi, Matteo|||0000-0001-6105-692X, Valdinoci, Enrico
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/118343
Acceso en línea:https://hdl.handle.net/2117/118343
https://dx.doi.org/10.1088/1361-6544/aab89d
Access Level:acceso abierto
Palabra clave:Differential equations
Mathematical physic
Superconductivity
Nonlocal Ginzburg-Landau-Allen-Cahn equation
Periodic media
Density and energy estimates
Planelike minimizers
Superconductivitat
Superconductors
Equacions diferencials
Física matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid::Superconductors
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spelling Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic mediaCozzi, Matteo|||0000-0001-6105-692XValdinoci, EnricoDifferential equationsMathematical physicSuperconductivityNonlocal Ginzburg-Landau-Allen-Cahn equationPeriodic mediaDensity and energy estimatesPlanelike minimizersSuperconductivitatSuperconductorsEquacions diferencialsFísica matemàticaÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integralsÀrees temàtiques de la UPC::Física::Física de l'estat sòlid::SuperconductorsWe consider here a nonlocal phase transition energy in a periodic medium and we construct solutions whose interfaces lie at a bounded distance from any given hyperplane. These solutions are either periodic or quasiperiodic, depending on the rational dependency of the normal direction to the reference hyperplane. Remarkably, the oscillations of the interfaces with respect to the reference hyperplane are bounded by a universal constant times the periodicity scale of the medium. This geometric property allows us to establish, in the limit, the existence of planelike nonlocal minimal surfaces in a periodic structure. The proofs rely on new optimal density and energy estimates. In particular, roughly speaking, the energy of phase transition minimizers is controlled, both from above and below, by the energy of one-dimensional transition layers.20182018-07-0120182018-06-22journal articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/118343https://dx.doi.org/10.1088/1361-6544/aab89dreponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/1183432026-05-27T15:37:01Z
dc.title.none.fl_str_mv Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
title Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
spellingShingle Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
Cozzi, Matteo|||0000-0001-6105-692X
Differential equations
Mathematical physic
Superconductivity
Nonlocal Ginzburg-Landau-Allen-Cahn equation
Periodic media
Density and energy estimates
Planelike minimizers
Superconductivitat
Superconductors
Equacions diferencials
Física matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid::Superconductors
title_short Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
title_full Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
title_fullStr Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
title_full_unstemmed Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
title_sort Planelike minimizers of nonlocal Ginzburg-Landau energies and fractional perimeters in periodic media
dc.creator.none.fl_str_mv Cozzi, Matteo|||0000-0001-6105-692X
Valdinoci, Enrico
author Cozzi, Matteo|||0000-0001-6105-692X
author_facet Cozzi, Matteo|||0000-0001-6105-692X
Valdinoci, Enrico
author_role author
author2 Valdinoci, Enrico
author2_role author
dc.subject.none.fl_str_mv Differential equations
Mathematical physic
Superconductivity
Nonlocal Ginzburg-Landau-Allen-Cahn equation
Periodic media
Density and energy estimates
Planelike minimizers
Superconductivitat
Superconductors
Equacions diferencials
Física matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid::Superconductors
topic Differential equations
Mathematical physic
Superconductivity
Nonlocal Ginzburg-Landau-Allen-Cahn equation
Periodic media
Density and energy estimates
Planelike minimizers
Superconductivitat
Superconductors
Equacions diferencials
Física matemàtica
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals
Àrees temàtiques de la UPC::Física::Física de l'estat sòlid::Superconductors
description We consider here a nonlocal phase transition energy in a periodic medium and we construct solutions whose interfaces lie at a bounded distance from any given hyperplane. These solutions are either periodic or quasiperiodic, depending on the rational dependency of the normal direction to the reference hyperplane. Remarkably, the oscillations of the interfaces with respect to the reference hyperplane are bounded by a universal constant times the periodicity scale of the medium. This geometric property allows us to establish, in the limit, the existence of planelike nonlocal minimal surfaces in a periodic structure. The proofs rely on new optimal density and energy estimates. In particular, roughly speaking, the energy of phase transition minimizers is controlled, both from above and below, by the energy of one-dimensional transition layers.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-07-01
2018
2018-06-22
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/118343
https://dx.doi.org/10.1088/1361-6544/aab89d
url https://hdl.handle.net/2117/118343
https://dx.doi.org/10.1088/1361-6544/aab89d
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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