{"id":"https://openalex.org/W3174121714","doi":"https://doi.org/10.1137/21m143011x","title":"Symmetry Properties of Minimizers of a Perturbed Dirichlet Energy with a Boundary Penalization","display_name":"Symmetry Properties of Minimizers of a Perturbed Dirichlet Energy with a Boundary Penalization","publication_year":2022,"publication_date":"2022-06-01","ids":{"openalex":"https://openalex.org/W3174121714","doi":"https://doi.org/10.1137/21m143011x","mag":"3174121714"},"language":"en","primary_location":{"id":"doi:10.1137/21m143011x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m143011x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://research-information.bris.ac.uk/en/publications/682c671e-b269-4b54-a5b4-9ce344570064","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058948920","display_name":"Giovanni Di Fratta","orcid":"https://orcid.org/0000-0003-0254-2957"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Giovanni Di Fratta","raw_affiliation_strings":["University of Bristol [Bristol] (Senate House, Tyndall Avenue, Bristol BS8 1TH - United Kingdom)"],"raw_orcid":"https://orcid.org/0000-0003-0254-2957","affiliations":[{"raw_affiliation_string":"University of Bristol [Bristol] (Senate House, Tyndall Avenue, Bristol BS8 1TH - United Kingdom)","institution_ids":["https://openalex.org/I36234482"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075821228","display_name":"Antonin Monteil","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I197681013","display_name":"Universit\u00e9 Paris-Est Cr\u00e9teil","ror":"https://ror.org/05ggc9x40","country_code":"FR","type":"education","lineage":["https://openalex.org/I197681013"]},{"id":"https://openalex.org/I4210144844","display_name":"Laboratoire d\u2019Analyse et de Math\u00e9matiques Appliqu\u00e9es","ror":"https://ror.org/0581g8849","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I197681013","https://openalex.org/I4210141950","https://openalex.org/I4210144844","https://openalex.org/I4210154111"]},{"id":"https://openalex.org/I4210154111","display_name":"Universit\u00e9 Gustave Eiffel","ror":"https://ror.org/03x42jk29","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Antonin Monteil","raw_affiliation_strings":["LAMA - Laboratoire Analyse et de Math\u00e9matiques Appliqu\u00e9es (Universit\u00e9 Gustave Eiffel, 5 boulevard Descartes, F-77454 Marne-la-Vall\u00e9e, France\r\nUniversit\u00e9 Paris-Est Cr\u00e9teil LAMA UMR CNRS 8050 UFR des Sciences et Technologie\r\nB\u00e2timent P3 - 4\u00e8me \u00e9tage -61, avenue du G\u00e9n\u00e9ral de Gaulle 94010 Cr\u00e9teil Cedex - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LAMA - Laboratoire Analyse et de Math\u00e9matiques Appliqu\u00e9es (Universit\u00e9 Gustave Eiffel, 5 boulevard Descartes, F-77454 Marne-la-Vall\u00e9e, France\r\nUniversit\u00e9 Paris-Est Cr\u00e9teil LAMA UMR CNRS 8050 UFR des Sciences et Technologie\r\nB\u00e2timent P3 - 4\u00e8me \u00e9tage -61, avenue du G\u00e9n\u00e9ral de Gaulle 94010 Cr\u00e9teil Cedex - France)","institution_ids":["https://openalex.org/I4210144844","https://openalex.org/I197681013","https://openalex.org/I1294671590","https://openalex.org/I4210154111"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017653216","display_name":"Valeriy Slastikov","orcid":"https://orcid.org/0000-0003-4550-4301"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Valeriy Slastikov","raw_affiliation_strings":["University of Bristol [Bristol] (Senate House, Tyndall Avenue, Bristol BS8 1TH - United Kingdom)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Bristol [Bristol] (Senate House, Tyndall Avenue, Bristol BS8 1TH - United Kingdom)","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7184,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.70916039,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"54","issue":"3","first_page":"3636","last_page":"3653"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9972000122070312,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9940000176429749,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.992900013923645,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.809040367603302},{"id":"https://openalex.org/keywords/symmetry-in-biology","display_name":"Symmetry in biology","score":0.6980981826782227},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6737738251686096},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6426293849945068},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.5853349566459656},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5234296321868896},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.4901943802833557},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.46461641788482666},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.4633287787437439},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.46227651834487915},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.42736709117889404},{"id":"https://openalex.org/keywords/dirichlets-energy","display_name":"Dirichlet's energy","score":0.42136555910110474},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.40694645047187805},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.3747554123401642},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.36493557691574097},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1748318374156952},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1459457278251648}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.809040367603302},{"id":"https://openalex.org/C64089718","wikidata":"https://www.wikidata.org/wiki/Q598159","display_name":"Symmetry in biology","level":2,"score":0.6980981826782227},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6737738251686096},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6426293849945068},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.5853349566459656},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5234296321868896},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.4901943802833557},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.46461641788482666},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.4633287787437439},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.46227651834487915},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.42736709117889404},{"id":"https://openalex.org/C96234433","wikidata":"https://www.wikidata.org/wiki/Q5280760","display_name":"Dirichlet's energy","level":4,"score":0.42136555910110474},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.40694645047187805},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.3747554123401642},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.36493557691574097},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1748318374156952},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1459457278251648}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/21m143011x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m143011x","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/682c671e-b269-4b54-a5b4-9ce344570064","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/682c671e-b269-4b54-a5b4-9ce344570064","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fratta, G D I, Monteil, A & Slastikov, V 2022, 'Symmetry Properties of Minimizers of a Perturbed Dirichlet Energy with a Boundary Penalization', SIAM Journal on Mathematical Analysis, vol. 54, no. 3, pp. 3636-3653. https://doi.org/10.1137/21M143011X","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/682c671e-b269-4b54-a5b4-9ce344570064","is_oa":true,"landing_page_url":"https://hdl.handle.net/1983/682c671e-b269-4b54-a5b4-9ce344570064","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Fratta, G D I, Monteil, A & Slastikov, V 2022, 'Symmetry Properties of Minimizers of a Perturbed Dirichlet Energy with a Boundary Penalization', SIAM Journal on Mathematical Analysis, vol. 54, no. 3, pp. 3636-3653. https://doi.org/10.1137/21M143011X","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:2106.15830","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2106.15830","pdf_url":"https://arxiv.org/pdf/2106.15830","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-04263223v1","is_oa":true,"landing_page_url":"https://hal.science/hal-04263223","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, 2022, 54 (3), ⟨10.1137/21M143011X⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/682c671e-b269-4b54-a5b4-9ce344570064","is_oa":true,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/682c671e-b269-4b54-a5b4-9ce344570064","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Fratta, G D I, Monteil, A & Slastikov, V 2022, 'Symmetry Properties of Minimizers of a Perturbed Dirichlet Energy with a Boundary Penalization', SIAM Journal on Mathematical Analysis, vol. 54, no. 3, pp. 3636-3653. https://doi.org/10.1137/21M143011X","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2568532592","display_name":"Taming Complexity in Partial Differential Systems","funder_award_id":"F65","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G278245057","display_name":null,"funder_award_id":"RPG-2018-438","funder_id":"https://openalex.org/F4320319993","funder_display_name":"Leverhulme Trust"}],"funders":[{"id":"https://openalex.org/F4320319993","display_name":"Leverhulme Trust","ror":"https://ror.org/012mzw131"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320321692","display_name":"Erwin Schr\u00f6dinger International Institute for Mathematics and Physics","ror":"https://ror.org/03prydq77"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W44035921","https://openalex.org/W1515685921","https://openalex.org/W1569061876","https://openalex.org/W1597469717","https://openalex.org/W1695002946","https://openalex.org/W1866311589","https://openalex.org/W1877525712","https://openalex.org/W1982357817","https://openalex.org/W2012435561","https://openalex.org/W2030911741","https://openalex.org/W2036297569","https://openalex.org/W2037417047","https://openalex.org/W2077461644","https://openalex.org/W2081121954","https://openalex.org/W2088081187","https://openalex.org/W2130432409","https://openalex.org/W2158172405","https://openalex.org/W2163659052","https://openalex.org/W2168284073","https://openalex.org/W2465001862","https://openalex.org/W2498106012","https://openalex.org/W2516435291","https://openalex.org/W2729805806","https://openalex.org/W2735806552","https://openalex.org/W2749988495","https://openalex.org/W2944133814","https://openalex.org/W2944463729","https://openalex.org/W2997651296","https://openalex.org/W3037085667","https://openalex.org/W3038681844","https://openalex.org/W3101523245","https://openalex.org/W3102960878","https://openalex.org/W3104761615","https://openalex.org/W3141027763","https://openalex.org/W3173081552","https://openalex.org/W4240361988","https://openalex.org/W4297791928"],"related_works":["https://openalex.org/W2158669000","https://openalex.org/W2020597526","https://openalex.org/W2283827582","https://openalex.org/W2045064573","https://openalex.org/W2013879581","https://openalex.org/W2055215183","https://openalex.org/W2988201549","https://openalex.org/W4394644391","https://openalex.org/W4285139269","https://openalex.org/W2342772136"],"abstract_inverted_index":{"We":[0,25,79],"consider":[1],"$\\mathbb{S}^2$-valued":[2],"maps":[3],"on":[4,23,98],"a":[5,9,36,44,58,82,96,99,130],"domain":[6],"$\\Omega\\subset\\mathbb{R}^N$":[7],"minimizing":[8],"perturbation":[10],"of":[11,31,39,61,68,74,107],"the":[12,28,40,62,72,75,118,126],"Dirichlet":[13],"energy":[14,52,120,128],"with":[15,87],"vertical":[16],"penalization":[17,22],"in":[18,35,129],"$\\Omega$":[19],"and":[20,65,101,105,125],"horizontal":[21],"$\\partial\\Omega$.":[24],"first":[26],"show":[27,102],"global":[29],"minimality":[30],"universal":[32],"constant":[33],"configurations":[34],"specific":[37],"range":[38],"physical":[41],"parameters":[42],"using":[43],"Poincar\u00e9-type":[45],"inequality.":[46],"Then":[47],"we":[48,91],"prove":[49,81],"that":[50],"any":[51],"minimizer":[53],"takes":[54],"its":[55],"values":[56],"into":[57],"fixed":[59],"half-meridian":[60],"sphere":[63],"$\\mathbb{S}^2$":[64],"deduce":[66],"uniqueness":[67],"minimizers":[69,86],"up":[70],"to":[71,95,117],"action":[73],"appropriate":[76],"symmetry":[77,104],"group.":[78],"also":[80],"comparison":[83],"principle":[84],"for":[85,121],"different":[88],"penalizations.":[89],"Finally,":[90],"apply":[92],"these":[93],"results":[94,113],"problem":[97],"ball":[100],"radial":[103],"monotonicity":[106],"minimizers.":[108],"In":[109],"dimension":[110],"$N=2$":[111],"our":[112],"can":[114],"be":[115],"applied":[116],"Oseen--Frank":[119],"nematic":[122],"liquid":[123],"crystals":[124],"micromagnetic":[127],"thin-film":[131],"regime.":[132]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-07-25T00:00:00"}