Area quasi-minimizing partitions with a graphical constraint: relaxation and two-dimensional partial regularity
We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to the geometrical constraint that their union is the subgraph of a function, whose graph is a free surface. The energy of a configuration is g...
Saved in:
| Published in | arXiv.org |
|---|---|
| Main Authors | , |
| Format | Paper Journal Article |
| Language | English |
| Published |
Ithaca
Cornell University Library, arXiv.org
06.10.2022
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 2331-8422 |
| DOI | 10.48550/arxiv.2107.13325 |
Cover
Loading…
| Abstract | We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to the geometrical constraint that their union is the subgraph of a function, whose graph is a free surface. The energy of a configuration is given by the weighted sum of the areas of the interfaces between the different regions, and a general volume-order term. We establish existence of minimizing configurations via relaxation of the energy involved, in any dimension. Moreover, we prove partial regularity results for volume-constrained minimizers in two space dimensions. Thin films of diblock copolymers are a possible application and motivation for considering this problem. |
|---|---|
| AbstractList | We consider a variational model for periodic partitions of the upper
half-space into three regions, where two of them have prescribed volume and are
subject to the geometrical constraint that their union is the subgraph of a
function, whose graph is a free surface. The energy of a configuration is given
by the weighted sum of the areas of the interfaces between the different
regions, and a general volume-order term. We establish existence of minimizing
configurations via relaxation of the energy involved, in any dimension.
Moreover, we prove partial regularity results for volume-constrained minimizers
in two space dimensions. Thin films of diblock copolymers are a possible
application and motivation for considering this problem. We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to the geometrical constraint that their union is the subgraph of a function, whose graph is a free surface. The energy of a configuration is given by the weighted sum of the areas of the interfaces between the different regions, and a general volume-order term. We establish existence of minimizing configurations via relaxation of the energy involved, in any dimension. Moreover, we prove partial regularity results for volume-constrained minimizers in two space dimensions. Thin films of diblock copolymers are a possible application and motivation for considering this problem. |
| Author | Bonacini, Marco Cristoferi, Riccardo |
| Author_xml | – sequence: 1 givenname: Marco surname: Bonacini fullname: Bonacini, Marco – sequence: 2 givenname: Riccardo surname: Cristoferi fullname: Cristoferi, Riccardo |
| BackLink | https://doi.org/10.48550/arXiv.2107.13325$$DView paper in arXiv https://doi.org/10.1007/s00332-022-09852-3$$DView published paper (Access to full text may be restricted) |
| BookMark | eNotkF1rwjAYhcPYYM75A3a1wK7r8tmmu5OxLxB24315a6JG2rQm6dT9-kXd1YHDw-Hw3KFr1zmD0AMlU6GkJM_gD_ZnyigpppRzJq_QiHFOMyUYu0WTELaEEJYXTEo-Qt3MG8C7AYLNWutsa3-tW-MefLTRdi7gvY0bDHjtod_YJTR4mdrowbr4gr1p4AAnEIPTOO67TNvWuJCahJ5nUnqzHhrwNh7v0c0KmmAm_zlGi_e3xetnNv_--HqdzTOQjGRCcMW1IHWhBPC6kFwqWEmQWpWilJoQMIItS220ISXVLK_lipe15lDTUig-Ro-X2bONqve2BX-sTlaqs5VEPF2I3ne7wYRYbbvBp9OhSmZymiuVE_4HdLtpEA |
| ContentType | Paper Journal Article |
| Copyright | 2022. 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. http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| Copyright_xml | – notice: 2022. 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. – notice: http://arxiv.org/licenses/nonexclusive-distrib/1.0 |
| DBID | 8FE 8FG ABJCF ABUWG AFKRA AZQEC BENPR BGLVJ CCPQU DWQXO HCIFZ L6V M7S PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS AKZ GOX |
| DOI | 10.48550/arxiv.2107.13325 |
| DatabaseName | ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central (Alumni) ProQuest Central UK/Ireland ProQuest Central Essentials ProQuest Technology Collection ProQuest One Community College ProQuest Central Korea SciTech Premium Collection ProQuest Engineering Collection Engineering Database ProQuest Central Premium ProQuest One Academic (New) Publicly Available Content Database ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection arXiv Mathematics arXiv.org |
| DatabaseTitle | Publicly Available Content Database Engineering Database Technology Collection ProQuest One Academic Middle East (New) 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 One Applied & Life Sciences ProQuest Engineering Collection ProQuest One Academic UKI Edition ProQuest Central Korea Materials Science & Engineering Collection ProQuest Central (New) ProQuest One Academic ProQuest One Academic (New) Engineering Collection |
| DatabaseTitleList | Publicly Available Content Database |
| Database_xml | – sequence: 1 dbid: GOX name: arXiv.org url: http://arxiv.org/find sourceTypes: Open Access Repository – sequence: 2 dbid: 8FG name: ProQuest Technology Collection url: https://search.proquest.com/technologycollection1 sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Physics |
| EISSN | 2331-8422 |
| ExternalDocumentID | 2107_13325 |
| 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 PHGZM PHGZT PIMPY PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS AKZ GOX |
| ID | FETCH-LOGICAL-a520-44383d40b784a3b75358af5a5d89495d00ae42c9dede091d26b5f39bd3ab19483 |
| IEDL.DBID | BENPR |
| IngestDate | Tue Jul 22 23:02:28 EDT 2025 Mon Jun 30 09:19:14 EDT 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | false |
| IsScholarly | false |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a520-44383d40b784a3b75358af5a5d89495d00ae42c9dede091d26b5f39bd3ab19483 |
| Notes | SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50 |
| OpenAccessLink | https://www.proquest.com/docview/2556168860?pq-origsite=%requestingapplication% |
| PQID | 2556168860 |
| PQPubID | 2050157 |
| ParticipantIDs | arxiv_primary_2107_13325 proquest_journals_2556168860 |
| PublicationCentury | 2000 |
| PublicationDate | 20221006 |
| PublicationDateYYYYMMDD | 2022-10-06 |
| PublicationDate_xml | – month: 10 year: 2022 text: 20221006 day: 06 |
| PublicationDecade | 2020 |
| PublicationPlace | Ithaca |
| PublicationPlace_xml | – name: Ithaca |
| PublicationTitle | arXiv.org |
| PublicationYear | 2022 |
| Publisher | Cornell University Library, arXiv.org |
| Publisher_xml | – name: Cornell University Library, arXiv.org |
| SSID | ssj0002672553 |
| Score | 1.8114955 |
| SecondaryResourceType | preprint |
| Snippet | We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to... We consider a variational model for periodic partitions of the upper half-space into three regions, where two of them have prescribed volume and are subject to... |
| SourceID | arxiv proquest |
| SourceType | Open Access Repository Aggregation Database |
| SubjectTerms | Block copolymers Configurations Constraints Mathematics - Analysis of PDEs Minimal surfaces Regularity Thin films Two dimensional models |
| SummonAdditionalLinks | – databaseName: arXiv.org dbid: GOX link: http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwdV2xTsMwELXaTiwIBKiFgjywBhLHdh22ClEqJGApUrfoHDtSB9LSplDx9dw5qRgQU6TIzvDO8r1n594xdp0lAGBUGfm0pNMqU0QgXRHRflyOvPbWUu3w84uevsmnuZp3GN_XwsB6t_hs_IHt5hb1yOgGVZRQXdYVgn7ZenydN5eTwYqrHf87DjlmePVnaw35YnLEDluix8dNZI5Zx1cnbDlGjsY_trBZRGTq8b74xtTBVxS_sAA4nYty4MFHmvDjBRE46uNQ33EqPNkFKDlUjtdfy8iRO3_jrNF8Bp_r0F-eutKdstnkYXY_jdqWBxEo1HGSjEOdjO3ISEgtSglloFSgnMlQybg4Bi9FkTnvPCZ6J7RVZZpZl4JNMmnSM9arlpXvM54VZVIgRi71pVQOMdfghEP2gAJOKT1g_QBUvmpcLXLCMA8YDthwj13eruhNTlZliTZGx-f_z7xgB4LKA-iCXQ9Zr15v_SUm7dpehcj9AEydmz0 priority: 102 providerName: Cornell University |
| Title | Area quasi-minimizing partitions with a graphical constraint: relaxation and two-dimensional partial regularity |
| URI | https://www.proquest.com/docview/2556168860 https://arxiv.org/abs/2107.13325 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwfV1LT4NAEN7YEhNvPtNqbfbglZY3ixejpo-YtDamJr2RhV2SHgQKVBsP_nZnFqoHEy8QIHD4Zpmdx-73EXITmJxz5ia6tBOsVrFY546IdfTHiS89GUW4d3g296avztPKXTUFt7JZVrn3icpRiyzGGvkQqbJMjzHPuMs3OqpGYXe1kdBoEQ1cMIMRrj2M5ouXnyqL5fnwol23MxV515AXu_X7ADIdfwD5GUpka-rWH2esZpjxMdEWPJfFCTmQ6Sk5VAsz4_KMZPcQ1dHNlpdrHWlA3tafMNnQHC2uhgzFSirlVDFPI-I0xpAPlR-qW4pbVXYKfMpTQauPTBfI519zcdSfgXOhFOlRx-6cLMej5eNUb0QSdO5C5ucg1ahwjMhnDrcjSD5cxhOXu4IFkPsIw-DSseJASCEhNBCWF7mJHUTC5pEZOMy-IO00S2WH0CBOzBgwErZMHFeAlTwuLAHxBqR8gH6XdBRQYV7zYISIYagw7JLeHruw-QfK8Ndil_8_viJHFm4qwLa81yPtqtjKa5jqq6hPWmw86TdWhavJ8wqOs6_RN9sKsIE |
| linkProvider | ProQuest |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV1LS8NAEB5qg-jNJ61W3YMe00feEUR8tLT2QZEKvYVNdiM92PRpq__J_-jMptWD4K2nQAJLmJmdnW925huAS7_COffsWJdmTNkqL9K5JSKd_HHsSkeGIfUOtztO_cV66tv9DHyte2GorHLtE5WjFklEOfISUWVVHM9zyrejsU5To-h2dT1CIzWLpvxYIGSb3jQeUb9XhlGr9h7q-mqqgM5thEoWcXMKqxy6nsXNEKN12-OxzW3h-QgWRLnMpWVEvpBC4lkqDCe0Y9MPhclDBPyeictugWaZGClkQbuvdrrPP0kdw3HxP8309lRxhZX4ZDl4LyKwcosIB2kit6Ze_fH96kCr7YHW5SM52YeMHB7AtqoDjaaHkNxhEMnGcz4d6MQ68jb4xLONjcjAlIUyStwyzhTRNSmYRRRh0qCJ2TWjzpil0jXjQ8Fmi0QXND4gpf5Il8HnRL5S9SsCgCPobUJ6x5AdJkOZA-ZHcSVCGQlTxpYt0CgcLgyB4Q0iTFR2HnJKUMEopd0ISIaBkmEeCmvZBastNw1-DeTk_88XsFPvtVtBq9FpnsKuQf0MVBHgFCA7m8zlGUYZs_B8pVsGwYat6RtEeOi2 |
| 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=Area+quasi-minimizing+partitions+with+a+graphical+constraint%3A+relaxation+and+two-dimensional+partial+regularity&rft.jtitle=arXiv.org&rft.au=Bonacini%2C+Marco&rft.au=Cristoferi%2C+Riccardo&rft.date=2022-10-06&rft.pub=Cornell+University+Library%2C+arXiv.org&rft.eissn=2331-8422&rft_id=info:doi/10.48550%2Farxiv.2107.13325 |