{"id":"https://openalex.org/W1972642191","doi":"https://doi.org/10.1137/130921994","title":"A Phase Field Model for the Optimization of the Willmore Energy in the Class of Connected Surfaces","display_name":"A Phase Field Model for the Optimization of the Willmore Energy in the Class of Connected Surfaces","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W1972642191","doi":"https://doi.org/10.1137/130921994","mag":"1972642191"},"language":"en","primary_location":{"id":"doi:10.1137/130921994","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130921994","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://durham-repository.worktribe.com/output/1443070","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065846980","display_name":"Patrick Dondl","orcid":"https://orcid.org/0000-0003-3035-7230"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Patrick W. Dondl","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048753607","display_name":"Luca Mugnai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Luca Mugnai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5034528628","display_name":"Matthias R\u00f6ger","orcid":"https://orcid.org/0000-0003-4381-4752"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Matthias R\u00f6ger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4295,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.80848726,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"46","issue":"2","first_page":"1610","last_page":"1632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991999864578247,"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":0.9991999864578247,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8129161596298218},{"id":"https://openalex.org/keywords/willmore-energy","display_name":"Willmore energy","score":0.7265845537185669},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.689643144607544},{"id":"https://openalex.org/keywords/social-connectedness","display_name":"Social connectedness","score":0.5973012447357178},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5392125844955444},{"id":"https://openalex.org/keywords/limit","display_name":"Limit (mathematics)","score":0.5027003288269043},{"id":"https://openalex.org/keywords/simply-connected-space","display_name":"Simply connected space","score":0.47244980931282043},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46554574370384216},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.4587869942188263},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.44702696800231934},{"id":"https://openalex.org/keywords/phase","display_name":"Phase (matter)","score":0.43120312690734863},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.424932062625885},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.4003520905971527},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.36757948994636536},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1874353289604187},{"id":"https://openalex.org/keywords/mean-curvature","display_name":"Mean curvature","score":0.15125587582588196},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12671881914138794},{"id":"https://openalex.org/keywords/curvature","display_name":"Curvature","score":0.10903829336166382},{"id":"https://openalex.org/keywords/mean-curvature-flow","display_name":"Mean curvature flow","score":0.07977715134620667},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.07825157046318054}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8129161596298218},{"id":"https://openalex.org/C39428390","wikidata":"https://www.wikidata.org/wiki/Q2581692","display_name":"Willmore energy","level":5,"score":0.7265845537185669},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.689643144607544},{"id":"https://openalex.org/C201943243","wikidata":"https://www.wikidata.org/wiki/Q7551008","display_name":"Social connectedness","level":2,"score":0.5973012447357178},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5392125844955444},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.5027003288269043},{"id":"https://openalex.org/C167204820","wikidata":"https://www.wikidata.org/wiki/Q912058","display_name":"Simply connected space","level":2,"score":0.47244980931282043},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46554574370384216},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4587869942188263},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.44702696800231934},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.43120312690734863},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.424932062625885},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.4003520905971527},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.36757948994636536},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1874353289604187},{"id":"https://openalex.org/C175017881","wikidata":"https://www.wikidata.org/wiki/Q1318998","display_name":"Mean curvature","level":3,"score":0.15125587582588196},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12671881914138794},{"id":"https://openalex.org/C195065555","wikidata":"https://www.wikidata.org/wiki/Q214881","display_name":"Curvature","level":2,"score":0.10903829336166382},{"id":"https://openalex.org/C127813850","wikidata":"https://www.wikidata.org/wiki/Q6803617","display_name":"Mean curvature flow","level":4,"score":0.07977715134620667},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.07825157046318054},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/130921994","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130921994","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:durham-repository.worktribe.com:1443070","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1443070","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},{"id":"pmh:oai:edoc.mpg.de:708508","is_oa":false,"landing_page_url":"http://edoc.mpg.de/708508","pdf_url":null,"source":{"id":"https://openalex.org/S4406922265","display_name":"Max Planck Institute for Plasma Physics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Mathematical Analysis, v.46, 1610-1632 (2014)","raw_type":"Article"}],"best_oa_location":{"id":"pmh:oai:durham-repository.worktribe.com:1443070","is_oa":true,"landing_page_url":"https://durham-repository.worktribe.com/output/1443070","pdf_url":null,"source":{"id":"https://openalex.org/S4306400188","display_name":"Durham Research Online (Durham University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I190082696","host_organization_name":"Durham University","host_organization_lineage":["https://openalex.org/I190082696"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal Article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.5400000214576721}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W7928106","https://openalex.org/W1497246097","https://openalex.org/W1603289878","https://openalex.org/W1840465687","https://openalex.org/W1866311589","https://openalex.org/W1987933126","https://openalex.org/W1990541396","https://openalex.org/W2014631005","https://openalex.org/W2029177929","https://openalex.org/W2053608680","https://openalex.org/W2063550694","https://openalex.org/W2082252207","https://openalex.org/W2086229068","https://openalex.org/W2086655386","https://openalex.org/W2086735769","https://openalex.org/W2093633673","https://openalex.org/W2150388881","https://openalex.org/W2159477611","https://openalex.org/W2162606802","https://openalex.org/W2963522119","https://openalex.org/W3104479934"],"related_works":["https://openalex.org/W3125761283","https://openalex.org/W2164081328","https://openalex.org/W1976722080","https://openalex.org/W3152831473","https://openalex.org/W3092556108","https://openalex.org/W1995672666","https://openalex.org/W2154176501","https://openalex.org/W3172628332","https://openalex.org/W2089945075","https://openalex.org/W2916943777"],"abstract_inverted_index":{"We":[0,85],"consider":[1],"the":[2,6,27,41,44,54,61,72,79,87,100,110,125],"problem":[3],"of":[4,43,53,63,65,90,96,109,119,121],"minimizing":[5],"Willmore":[7,80],"energy":[8],"connected":[9,107],"surfaces":[10],"with":[11],"prescribed":[12],"surface":[13,28,45,55],"area":[14,73],"which":[15],"are":[16,82],"confined":[17],"to":[18,38,105,124],"a":[19,30,93,117],"finite":[20],"container.":[21],"To":[22],"this":[23,113],"end,":[24],"we":[25,115],"approximate":[26],"by":[29,60,92],"phase":[31,98],"field":[32],"function":[33],"$u$":[34],"taking":[35],"values":[36],"close":[37],"+1":[39],"on":[40,48],"inside":[42],"and":[46],"-1":[47],"its":[49],"outside.":[50],"The":[51],"confinement":[52],"is":[56],"now":[57],"simply":[58],"given":[59],"domain":[62],"definition":[64],"$u$.":[66],"A":[67],"diffuse":[68],"interface":[69,127],"approximation":[70],"for":[71,78],"functional,":[74],"as":[75,77],"well":[76,83],"energy,":[81],"known.":[84],"address":[86],"topological":[88],"constraint":[89],"connectedness":[91],"nested":[94],"minimization":[95],"two":[97],"fields,":[99],"second":[101],"one":[102],"being":[103],"used":[104],"identify":[106],"components":[108],"surface.":[111],"In":[112],"article,":[114],"provide":[116],"proof":[118],"Gamma-convergence":[120],"our":[122],"model":[123],"sharp":[126],"limit.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
