{"id":"https://openalex.org/W2963057656","doi":"https://doi.org/10.1137/110821469","title":"Boundary Effects in the Gradient Theory of Phase Transitions","display_name":"Boundary Effects in the Gradient Theory of Phase Transitions","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2963057656","doi":"https://doi.org/10.1137/110821469","mag":"2963057656"},"language":"en","primary_location":{"id":"doi:10.1137/110821469","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110821469","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069901792","display_name":"Lorenzo Bertini","orcid":"https://orcid.org/0000-0002-1382-6616"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Lorenzo Bertini","raw_affiliation_strings":["Dipartimento di Matematica, SAPIENZA Universit\u00e0 di Roma, P.le Aldo Moro 5, 00185 Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, SAPIENZA Universit\u00e0 di Roma, P.le Aldo Moro 5, 00185 Roma, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042527170","display_name":"Paolo Butt\u00e0","orcid":"https://orcid.org/0000-0002-3193-4282"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paolo Butt\u00e0","raw_affiliation_strings":["Dipartimento di Matematica, SAPIENZA Universit\u00e0 di Roma, P.le Aldo Moro 5, 00185 Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, SAPIENZA Universit\u00e0 di Roma, P.le Aldo Moro 5, 00185 Roma, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062826979","display_name":"Adriana Garroni","orcid":"https://orcid.org/0000-0003-0742-2524"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Adriana Garroni","raw_affiliation_strings":["Dipartimento di Matematica, SAPIENZA Universit\u00e0 di Roma, P.le Aldo Moro 5, 00185 Roma, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, SAPIENZA Universit\u00e0 di Roma, P.le Aldo Moro 5, 00185 Roma, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5069901792"],"corresponding_institution_ids":["https://openalex.org/I861853513"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.37029432,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"44","issue":"2","first_page":"926","last_page":"945"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12202","display_name":"nanoparticles nucleation surface interactions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10591","display_name":"Theoretical and Computational Physics","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11520","display_name":"Advanced Thermodynamics and Statistical Mechanics","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear 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":0.770596981048584},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.7433754205703735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6487463116645813},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.636283814907074},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5615444779396057},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5308687686920166},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.4841940701007843},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4699832499027252},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4569743871688843},{"id":"https://openalex.org/keywords/scaling-limit","display_name":"Scaling limit","score":0.45125237107276917},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4468388557434082},{"id":"https://openalex.org/keywords/phase-transition","display_name":"Phase transition","score":0.42740535736083984},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.4254087209701538},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"Asymptotic analysis","score":0.4200612008571625},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.34346386790275574},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.22152629494667053},{"id":"https://openalex.org/keywords/condensed-matter-physics","display_name":"Condensed matter physics","score":0.12538692355155945}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.770596981048584},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.7433754205703735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6487463116645813},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.636283814907074},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5615444779396057},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5308687686920166},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.4841940701007843},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4699832499027252},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4569743871688843},{"id":"https://openalex.org/C24084028","wikidata":"https://www.wikidata.org/wiki/Q7429781","display_name":"Scaling limit","level":3,"score":0.45125237107276917},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4468388557434082},{"id":"https://openalex.org/C149288129","wikidata":"https://www.wikidata.org/wiki/Q185357","display_name":"Phase transition","level":2,"score":0.42740535736083984},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.4254087209701538},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.4200612008571625},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.34346386790275574},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.22152629494667053},{"id":"https://openalex.org/C26873012","wikidata":"https://www.wikidata.org/wiki/Q214781","display_name":"Condensed matter physics","level":1,"score":0.12538692355155945},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/110821469","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110821469","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:iris.uniroma1.it:11573/443417","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/443417","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.8999999761581421}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W169751261","https://openalex.org/W286983075","https://openalex.org/W631645091","https://openalex.org/W649818166","https://openalex.org/W1987723981","https://openalex.org/W2046528357","https://openalex.org/W2051227242","https://openalex.org/W2089345349","https://openalex.org/W2101472595","https://openalex.org/W2107729689","https://openalex.org/W2117880605","https://openalex.org/W2483288645","https://openalex.org/W3100177997","https://openalex.org/W3106020017"],"related_works":["https://openalex.org/W2126120377","https://openalex.org/W3101030220","https://openalex.org/W102371419","https://openalex.org/W1630264349","https://openalex.org/W2072609575","https://openalex.org/W1570562499","https://openalex.org/W2016612443","https://openalex.org/W4226218432","https://openalex.org/W4387315775","https://openalex.org/W3098670919"],"abstract_inverted_index":{"We":[0,24,69],"consider":[1],"the":[2,14,26,31,45,57,60,83,89,100,104,119,136],"van":[3],"der":[4],"Waals'":[5],"free":[6,39,120],"energy":[7,121],"functional,":[8],"with":[9,19],"scaling":[10],"parameter":[11],"$\\varepsilon$,":[12],"in":[13,52,98],"plane":[15],"domain":[16],"$\\mathbb{R}_+\\times":[17],"\\mathbb{R}_+$,":[18],"inhomogeneous":[20],"Dirichlet":[21],"boundary":[22,40,90],"conditions.":[23],"impose":[25],"two":[27],"stable":[28],"phases":[29,62],"on":[30,42,47],"horizontal":[32],"boundaries":[33],"$\\mathbb{R}_+":[34],"\\times\\{0\\}$":[35],"and":[36,38,91],"$\\mathbb{R}_+\\times\\{+\\infty\\}$,":[37],"conditions":[41],"$\\{+\\infty\\}\\times\\mathbb{R}_+$.":[43],"Finally,":[44],"datum":[46],"$\\{0\\}\\times":[48],"\\mathbb{R}_+$":[49],"is":[50,63,110,128],"chosen":[51],"such":[53,78,126],"a":[54,74,96,124],"way":[55],"that":[56,71],"interface":[58],"between":[59],"pure":[61],"pinned":[64],"at":[65],"some":[66],"point":[67],"$(0,y)$.":[68],"show":[70],"there":[72],"exists":[73],"critical":[75],"scaling,":[76],"$y=y_\\varepsilon$,":[77],"that,":[79],"as":[80],"$\\varepsilon\\to":[81],"0$,":[82],"competing":[84],"effects":[85],"of":[86,93,103,114,118,139],"repulsion":[87],"from":[88],"penalization":[92],"gradients":[94],"play":[95],"role":[97],"determining":[99],"optimal":[101],"shape":[102],"(properly":[105],"rescaled)":[106],"interface.":[107],"This":[108],"result":[109],"achieved":[111],"by":[112],"means":[113],"an":[115],"asymptotic":[116,137],"development":[117],"functional.":[122],"As":[123],"consequence,":[125],"analysis":[127],"not":[129],"restricted":[130],"to":[131],"minimizers":[132],"but":[133],"also":[134],"encodes":[135],"probability":[138],"fluctuations.":[140]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
