{"id":"https://openalex.org/W2095367910","doi":"https://doi.org/10.1016/0168-0072(95)00034-8","title":"Effective content of the calculus of variations I: Semi-continuity and the chattering lemma","display_name":"Effective content of the calculus of variations I: Semi-continuity and the chattering lemma","publication_year":1996,"publication_date":"1996-04-01","ids":{"openalex":"https://openalex.org/W2095367910","doi":"https://doi.org/10.1016/0168-0072(95)00034-8","mag":"2095367910"},"language":"en","primary_location":{"id":"doi:10.1016/0168-0072(95)00034-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0168-0072(95)00034-8","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/0168-0072(95)00034-8","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045922260","display_name":"Xiaolin Ge","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xiaolin Ge","raw_affiliation_strings":["Mathematical Sciences Institute, Cornell University, Ithaca, NY 14850, USA"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Institute, Cornell University, Ithaca, NY 14850, USA","institution_ids":["https://openalex.org/I205783295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082347461","display_name":"Anil Nerode","orcid":null},"institutions":[{"id":"https://openalex.org/I205783295","display_name":"Cornell University","ror":"https://ror.org/05bnh6r87","country_code":"US","type":"education","lineage":["https://openalex.org/I205783295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Anil Nerode","raw_affiliation_strings":["Mathematical Sciences Institute, Cornell University, Ithaca, NY 14850, USA"],"affiliations":[{"raw_affiliation_string":"Mathematical Sciences Institute, Cornell University, Ithaca, NY 14850, USA","institution_ids":["https://openalex.org/I205783295"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045922260"],"corresponding_institution_ids":["https://openalex.org/I205783295"],"apc_list":{"value":3390,"currency":"USD","value_usd":3390},"apc_paid":{"value":3390,"currency":"USD","value_usd":3390},"fwci":4.0469,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.94161208,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"78","issue":"1-3","first_page":"127","last_page":"146"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991000294685364,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991000294685364,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9408000111579895,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.930400013923645,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/lemma","display_name":"Lemma (botany)","score":0.8847235441207886},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6625238060951233},{"id":"https://openalex.org/keywords/content","display_name":"Content (measure theory)","score":0.6342942714691162},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5637985467910767},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.552699089050293},{"id":"https://openalex.org/keywords/differential-calculus","display_name":"Differential calculus","score":0.5009710788726807},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4331305921077728},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.427923321723938},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.33531662821769714},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2982889413833618},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22456219792366028}],"concepts":[{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.8847235441207886},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6625238060951233},{"id":"https://openalex.org/C2778152352","wikidata":"https://www.wikidata.org/wiki/Q5165061","display_name":"Content (measure theory)","level":2,"score":0.6342942714691162},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5637985467910767},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.552699089050293},{"id":"https://openalex.org/C56802139","wikidata":"https://www.wikidata.org/wiki/Q149999","display_name":"Differential calculus","level":2,"score":0.5009710788726807},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4331305921077728},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.427923321723938},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.33531662821769714},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2982889413833618},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22456219792366028},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/0168-0072(95)00034-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0168-0072(95)00034-8","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1016/0168-0072(95)00034-8","is_oa":true,"landing_page_url":"https://doi.org/10.1016/0168-0072(95)00034-8","pdf_url":null,"source":{"id":"https://openalex.org/S172477885","display_name":"Annals of Pure and Applied Logic","issn_l":"0168-0072","issn":["0168-0072","1873-2461"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Annals of Pure and Applied Logic","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W220096824","https://openalex.org/W237194509","https://openalex.org/W382151588","https://openalex.org/W615533861","https://openalex.org/W1497475168","https://openalex.org/W1594563152","https://openalex.org/W1599845971","https://openalex.org/W1653619892","https://openalex.org/W1908291764","https://openalex.org/W1975452830","https://openalex.org/W2043723475","https://openalex.org/W2056414301","https://openalex.org/W2067914884","https://openalex.org/W2079942928","https://openalex.org/W2333253576","https://openalex.org/W2340279101","https://openalex.org/W2578658812","https://openalex.org/W2889680710","https://openalex.org/W4231629838","https://openalex.org/W4239316923","https://openalex.org/W4239497877","https://openalex.org/W6808814299","https://openalex.org/W6990055222"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W2949964783","https://openalex.org/W4308265086","https://openalex.org/W2106889256","https://openalex.org/W2982363256","https://openalex.org/W2974000959","https://openalex.org/W1605511414","https://openalex.org/W2043671984"],"abstract_inverted_index":{"The":[0],"content":[1,32,66],"of":[2,8,17,33,36,49,53,67,70],"existence":[3],"theorems":[4],"in":[5],"the":[6,29,34,50,63,68],"calculus":[7],"variations":[9],"has":[10,19,24],"been":[11,20,25],"explored":[12],"and":[13,40,56],"an":[14,46],"effective":[15,47],"treatment":[16],"semi-continuity":[18],"achieved.":[21],"An":[22],"algorithm":[23],"developed":[26],"which":[27],"captures":[28],"natural":[30],"algorithmic":[31],"notion":[35],"a":[37],"semi-continuous":[38],"function":[39],"this":[41],"is":[42],"used":[43],"to":[44],"obtain":[45],"version":[48],"\u201cchattering":[51],"lemma\u201d":[52],"control":[54],"theory":[55,69],"ordinary":[57],"differential":[58],"equations.":[59],"This":[60],"lemma":[61],"reveals":[62],"main":[64],"computational":[65],"relaxed":[71],"optimal":[72],"control.":[73]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}