{"id":"https://openalex.org/W2085189045","doi":"https://doi.org/10.1137/080743342","title":"Necessary Conditions for Solutions to Variational Problems","display_name":"Necessary Conditions for Solutions to Variational Problems","publication_year":2009,"publication_date":"2009-11-11","ids":{"openalex":"https://openalex.org/W2085189045","doi":"https://doi.org/10.1137/080743342","mag":"2085189045"},"language":"en","primary_location":{"id":"doi:10.1137/080743342","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080743342","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10281/8664","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048687668","display_name":"Arrigo Cellina","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"A. Cellina","raw_affiliation_strings":["arrigo.cellina@unimib.it and m.mazzola7@campus.unimib.it#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"arrigo.cellina@unimib.it and m.mazzola7@campus.unimib.it#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061876866","display_name":"Marco Mazzola","orcid":"https://orcid.org/0000-0001-6445-0279"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Mazzola","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":0.7969,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70815975,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"48","issue":"5","first_page":"2977","last_page":"2983"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9977999925613403,"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"}},"topics":[{"id":"https://openalex.org/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9977999925613403,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9958999752998352,"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":0.9952999949455261,"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":0.8791579604148865},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.8078947067260742},{"id":"https://openalex.org/keywords/pontryagins-minimum-principle","display_name":"Pontryagin's minimum principle","score":0.7615426778793335},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6936910152435303},{"id":"https://openalex.org/keywords/omega","display_name":"Omega","score":0.6544786095619202},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.6211302876472473},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5913900136947632},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4251518249511719},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36963343620300293},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.3637729287147522},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3481002449989319},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.33724188804626465},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32745006680488586},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.102824866771698},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0578952431678772}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8791579604148865},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.8078947067260742},{"id":"https://openalex.org/C141803461","wikidata":"https://www.wikidata.org/wiki/Q3491629","display_name":"Pontryagin's minimum principle","level":3,"score":0.7615426778793335},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6936910152435303},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.6544786095619202},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.6211302876472473},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5913900136947632},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4251518249511719},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36963343620300293},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.3637729287147522},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3481002449989319},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.33724188804626465},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32745006680488586},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.102824866771698},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0578952431678772},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/080743342","is_oa":false,"landing_page_url":"https://doi.org/10.1137/080743342","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:boa.unimib.it:10281/8664","is_oa":true,"landing_page_url":"http://hdl.handle.net/10281/8664","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:boa.unimib.it:10281/8664","is_oa":true,"landing_page_url":"http://hdl.handle.net/10281/8664","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":null,"raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1520895637","https://openalex.org/W2002687104","https://openalex.org/W2007265109","https://openalex.org/W4239732081"],"related_works":["https://openalex.org/W2771042763","https://openalex.org/W2155570364","https://openalex.org/W4211240924","https://openalex.org/W4302321938","https://openalex.org/W4292923857","https://openalex.org/W2031281152","https://openalex.org/W2543201876","https://openalex.org/W2511035558","https://openalex.org/W162218241","https://openalex.org/W2792440356"],"abstract_inverted_index":{"We":[0],"prove":[1],"necessary":[2],"conditions":[3],"for":[4,23],"a":[5,19,28],"solution":[6],"u":[7],"to":[8],"the":[9,16],"problem":[10],"of":[11,18],"minimizing":[12],"$\\int_\\Omega[f(\\|\\nabla":[13],"v(x)\\|)+g(x,v(x))]dx$":[14],"in":[15],"form":[17],"Pontryagin":[20],"maximum":[21],"principle,":[22],"f":[24],"convex":[25],"and":[26],"satisfying":[27],"growth":[29],"assumption,":[30],"but":[31],"without":[32],"assuming":[33],"differentiability.":[34]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}