{"id":"https://openalex.org/W4385335525","doi":"https://doi.org/10.1137/22m1519018","title":"Critical Points of Degenerate Polyconvex Energies","display_name":"Critical Points of Degenerate Polyconvex Energies","publication_year":2023,"publication_date":"2023-07-28","ids":{"openalex":"https://openalex.org/W4385335525","doi":"https://doi.org/10.1137/22m1519018"},"language":"en","primary_location":{"id":"doi:10.1137/22m1519018","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1519018","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/A5028191336","display_name":"Riccardo Tione","orcid":"https://orcid.org/0000-0002-0094-5923"},"institutions":[{"id":"https://openalex.org/I4210091327","display_name":"Max Planck Institute for Mathematics in the Sciences","ror":"https://ror.org/00ez2he07","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210091327"]},{"id":"https://openalex.org/I4210119712","display_name":"Max Planck Institute for Mathematics","ror":"https://ror.org/02dh8ja68","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210119712"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Riccardo Tione","raw_affiliation_strings":["Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany"],"affiliations":[{"raw_affiliation_string":"Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany","institution_ids":["https://openalex.org/I4210119712","https://openalex.org/I4210091327"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5028191336"],"corresponding_institution_ids":["https://openalex.org/I4210091327","https://openalex.org/I4210119712"],"apc_list":null,"apc_paid":null,"fwci":0.5593,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.62200314,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"55","issue":"4","first_page":"3205","last_page":"3225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9941999912261963,"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"}},"topics":[{"id":"https://openalex.org/T12396","display_name":"Advanced Differential Equations and Dynamical Systems","score":0.9941999912261963,"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"}},{"id":"https://openalex.org/T11151","display_name":"Advanced Topology and Set Theory","score":0.9937999844551086,"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"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9937000274658203,"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":0.885231614112854},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6639264822006226},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6603548526763916},{"id":"https://openalex.org/keywords/differential-inclusion","display_name":"Differential inclusion","score":0.6500004529953003},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6263139247894287},{"id":"https://openalex.org/keywords/zero","display_name":"Zero (linguistics)","score":0.5944636464118958},{"id":"https://openalex.org/keywords/degenerate-energy-levels","display_name":"Degenerate energy levels","score":0.5550225973129272},{"id":"https://openalex.org/keywords/critical-point","display_name":"Critical point (mathematics)","score":0.47052276134490967},{"id":"https://openalex.org/keywords/almost-everywhere","display_name":"Almost everywhere","score":0.4565824866294861},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.44423699378967285},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3233506977558136}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.885231614112854},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6639264822006226},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6603548526763916},{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.6500004529953003},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6263139247894287},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.5944636464118958},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5550225973129272},{"id":"https://openalex.org/C196298200","wikidata":"https://www.wikidata.org/wiki/Q577705","display_name":"Critical point (mathematics)","level":2,"score":0.47052276134490967},{"id":"https://openalex.org/C27142425","wikidata":"https://www.wikidata.org/wiki/Q1139334","display_name":"Almost everywhere","level":2,"score":0.4565824866294861},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.44423699378967285},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3233506977558136},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","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},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/22m1519018","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/22m1519018","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W140204898","https://openalex.org/W1144576613","https://openalex.org/W1507421217","https://openalex.org/W1555984062","https://openalex.org/W1603765353","https://openalex.org/W1983814397","https://openalex.org/W2001750022","https://openalex.org/W2013942539","https://openalex.org/W2031854460","https://openalex.org/W2036957001","https://openalex.org/W2081480663","https://openalex.org/W2083636316","https://openalex.org/W2084478435","https://openalex.org/W2088793810","https://openalex.org/W2167330745","https://openalex.org/W2287737683","https://openalex.org/W2323867769","https://openalex.org/W2793869493","https://openalex.org/W2889046694","https://openalex.org/W3022263217","https://openalex.org/W3098625336","https://openalex.org/W3127448507","https://openalex.org/W3155639669","https://openalex.org/W4206376869"],"related_works":["https://openalex.org/W2013232734","https://openalex.org/W2066616184","https://openalex.org/W1516195074","https://openalex.org/W2046733069","https://openalex.org/W2328195414","https://openalex.org/W4292443097","https://openalex.org/W2949265104","https://openalex.org/W2028171833","https://openalex.org/W1995126306","https://openalex.org/W2037905349"],"abstract_inverted_index":{"We":[0,72],"study":[1],"critical":[2,6,29],"and":[3,12,46,84],"stationary,":[4],"i.e.,":[5],"with":[7,31,101],"respect":[8,102],"to":[9,67,81,99,103],"both":[10],"inner":[11],"outer":[13],"variations,":[14],"points":[15,30,49],"of":[16,19,43,77],"polyconvex":[17,104],"functionals":[18],"the":[20,68,78,95],"form":[21],"for":[22],".":[23,71,90],"In":[24],"particular,":[25],"we":[26,92],"show":[27,93],"that":[28,47,94],"a.e.":[32],"have":[33,50],"locally":[34],"constant":[35,51],"determinant":[36,52],"except":[37],"in":[38],"a":[39,59],"relatively":[40],"closed":[41],"set":[42],"measure":[44],"zero,":[45],"stationary":[48],"almost":[53],"everywhere.":[54],"This":[55],"is":[56,108],"deduced":[57],"from":[58],"more":[60],"general":[61],"result":[62,80],"concerning":[63],"solutions":[64,89],",":[65,66],"linearized":[69],"problem":[70],"also":[73],"present":[74],"some":[75],"generalization":[76],"original":[79],"higher":[82],"dimensions":[83],"assuming":[85],"further":[86],"regularity":[87],"on":[88],"Finally,":[91],"differential":[96],"inclusion":[97],"associated":[98],"stationarity":[100],"energies":[105],"as":[106],"above":[107],"rigid.":[109]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2025-12-24T23:09:58.560324","created_date":"2025-10-10T00:00:00"}
