{"id":"https://openalex.org/W4405157024","doi":"https://doi.org/10.1007/s00332-024-10114-7","title":"$$\\Gamma $$-Convergence for Plane to Wrinkles Transition Problem","display_name":"$$\\Gamma $$-Convergence for Plane to Wrinkles Transition Problem","publication_year":2024,"publication_date":"2024-12-09","ids":{"openalex":"https://openalex.org/W4405157024","doi":"https://doi.org/10.1007/s00332-024-10114-7"},"language":"en","primary_location":{"id":"doi:10.1007/s00332-024-10114-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-024-10114-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-024-10114-7.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00332-024-10114-7.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052145055","display_name":"Peter Bella","orcid":"https://orcid.org/0000-0002-1660-1711"},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Peter Bella","raw_affiliation_strings":["Technische Universit\u00e4t Dortmund Fakult\u00e4t f\u00fcr Mathematik, 44227, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Dortmund Fakult\u00e4t f\u00fcr Mathematik, 44227, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033152280","display_name":"Roberta Marziani","orcid":"https://orcid.org/0000-0002-5846-8082"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Roberta Marziani","raw_affiliation_strings":["Dipartimento di Ingegneria dell\u2019 Informazione e Scienze Matematiche, 53100, Siena, Italy","Dipartimento di Ingegneria dell' Informazione e Scienze Matematiche, 53100, Siena, Italy"],"affiliations":[{"raw_affiliation_string":"Dipartimento di Ingegneria dell\u2019 Informazione e Scienze Matematiche, 53100, Siena, Italy","institution_ids":[]},{"raw_affiliation_string":"Dipartimento di Ingegneria dell' Informazione e Scienze Matematiche, 53100, Siena, Italy","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5052145055"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":{"value":2290,"currency":"EUR","value_usd":2890},"fwci":0.6708,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66922623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":100},"biblio":{"volume":"35","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11737","display_name":"Advanced Materials and Mechanics","score":0.9866999983787537,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11870","display_name":"Structural Analysis and Optimization","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12504","display_name":"Mathematics and Applications","score":0.9670000076293945,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/convergence","display_name":"Convergence (economics)","score":0.5356964468955994},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49137917160987854},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.45630592107772827},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41704633831977844},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.35627496242523193},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35309159755706787},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.33648988604545593},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3359729051589966},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.32869964838027954},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.09842953085899353}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5356964468955994},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49137917160987854},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.45630592107772827},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41704633831977844},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.35627496242523193},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35309159755706787},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.33648988604545593},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3359729051589966},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.32869964838027954},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.09842953085899353},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00332-024-10114-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-024-10114-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-024-10114-7.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s00332-024-10114-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00332-024-10114-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00332-024-10114-7.pdf","source":{"id":"https://openalex.org/S131276044","display_name":"Journal of Nonlinear Science","issn_l":"0938-8974","issn":["0938-8974","1432-1467"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Nonlinear Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320329559","display_name":"Technische Universit\u00e4t Dortmund","ror":"https://ror.org/01k97gp34"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4405157024.pdf"},"referenced_works_count":60,"referenced_works":["https://openalex.org/W1480714962","https://openalex.org/W1603082330","https://openalex.org/W1738603105","https://openalex.org/W1798492768","https://openalex.org/W1966779513","https://openalex.org/W1987715719","https://openalex.org/W1991423628","https://openalex.org/W1994489266","https://openalex.org/W1996873638","https://openalex.org/W1999915508","https://openalex.org/W2006906080","https://openalex.org/W2010296342","https://openalex.org/W2012274761","https://openalex.org/W2015296483","https://openalex.org/W2015334364","https://openalex.org/W2022149301","https://openalex.org/W2032458364","https://openalex.org/W2033875024","https://openalex.org/W2061979831","https://openalex.org/W2062486037","https://openalex.org/W2076008129","https://openalex.org/W2092688833","https://openalex.org/W2131698150","https://openalex.org/W2153216552","https://openalex.org/W2163055580","https://openalex.org/W2170014048","https://openalex.org/W2272229200","https://openalex.org/W2343438726","https://openalex.org/W2550737491","https://openalex.org/W2589539345","https://openalex.org/W2763837670","https://openalex.org/W2783742761","https://openalex.org/W2789296976","https://openalex.org/W2940885460","https://openalex.org/W2948914873","https://openalex.org/W2963155315","https://openalex.org/W2963678069","https://openalex.org/W2963679354","https://openalex.org/W3099343978","https://openalex.org/W3099667473","https://openalex.org/W3101343426","https://openalex.org/W3101363292","https://openalex.org/W3101837579","https://openalex.org/W3102615182","https://openalex.org/W3105377852","https://openalex.org/W3124165314","https://openalex.org/W3130812248","https://openalex.org/W3190532507","https://openalex.org/W3206034718","https://openalex.org/W4247809122","https://openalex.org/W4255839052","https://openalex.org/W4312938196","https://openalex.org/W4313678579","https://openalex.org/W4362667207","https://openalex.org/W4380048486","https://openalex.org/W4380085937","https://openalex.org/W4383721654","https://openalex.org/W4385985979","https://openalex.org/W4386784551","https://openalex.org/W4404379864"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W1517908938","https://openalex.org/W2281834912","https://openalex.org/W1489941249","https://openalex.org/W3123492739","https://openalex.org/W4320486059","https://openalex.org/W2494168571","https://openalex.org/W2033096984","https://openalex.org/W3121191496","https://openalex.org/W1550676882"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"consider":[2],"a":[3,14,146],"variational":[4],"problem":[5,56],"modeling":[6],"transition":[7],"between":[8],"flat":[9],"and":[10,18,59,63,94,130,148],"wrinkled":[11],"region":[12],"in":[13,47],"thin":[15],"elastic":[16],"sheet":[17,30],"identify":[19],"the":[20,29,37,41,68,90,97,106,110,139,151],"$$\\Gamma":[21,69,111],"$$":[22,71,113],"<mml:math":[23,72,114],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[24,73,115],"<mml:mi>\u0393</mml:mi>":[25,75,117],"</mml:math>":[26,80,122],"-limit":[27],"as":[28],"thickness":[31],"goes":[32],"to":[33,85],"0,":[34],"thus":[35],"extending":[36],"previous":[38],"work":[39],"of":[40,105,127,133,145,150],"first":[42,83],"author":[43],"(Bella":[44],"et":[45],"al.":[46],"Arch":[48],"Ration":[49],"Mech":[50],"Anal":[51],"218(1):163\u2013217,":[52],"2015).":[53],"The":[54,103],"limiting":[55,140],"is":[57],"scalar":[58],"convex,":[60],"but":[61],"constrained":[62],"posed":[64],"for":[65,109,138,153],"measures.":[66],"For":[67],"-\\liminf":[70],"<mml:mrow>":[74,116],"<mml:mo>-</mml:mo>":[76,118],"<mml:mo>lim":[77,119],"inf</mml:mo>":[78],"</mml:mrow>":[79,121],"inequality,":[81],"we":[82,142],"pass":[84],"quadratic":[86,128],"variables":[87,129],"so":[88],"that":[89],"constraint":[91],"becomes":[92],"linear,":[93],"then":[95],"obtain":[96],"lower":[98],"bound":[99],"using":[100],"Reshetnyak\u2019s":[101],"theorem.":[102],"construction":[104,135],"recovery":[107],"sequence":[108],"-\\limsup":[112],"sup</mml:mo>":[120],"inequality":[123],"relies":[124],"on":[125],"mollification":[126],"careful":[131],"choice":[132],"multiple":[134],"parameters.":[136],"Eventually":[137],"problem,":[141],"show":[143],"existence":[144],"minimizer":[147],"equipartition":[149],"energy":[152],"each":[154],"frequency.":[155]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1}],"updated_date":"2026-03-08T08:50:53.379069","created_date":"2025-10-10T00:00:00"}