{"id":"https://openalex.org/W2021504747","doi":"https://doi.org/10.1137/050630076","title":"Some New Regularity Properties for the Minimal Time Function","display_name":"Some New Regularity Properties for the Minimal Time Function","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2021504747","doi":"https://doi.org/10.1137/050630076","mag":"2021504747"},"language":"en","primary_location":{"id":"doi:10.1137/050630076","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630076","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/11577/1561047","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101437440","display_name":"Giovanni Colombo","orcid":"https://orcid.org/0000-0002-0675-0465"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giovanni Colombo","raw_affiliation_strings":["Dipartimento di Matematica Pura e Applicata, Universit\u00e0 di Padova, via Belzoni 7, 35131 Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Pura e Applicata, Universit\u00e0 di Padova, via Belzoni 7, 35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089252689","display_name":"Antonio Marigonda","orcid":"https://orcid.org/0000-0003-3242-7474"},"institutions":[{"id":"https://openalex.org/I138689650","display_name":"University of Padua","ror":"https://ror.org/00240q980","country_code":"IT","type":"education","lineage":["https://openalex.org/I138689650"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Antonio Marigonda","raw_affiliation_strings":["Dipartimento di Matematica Pura e Applicata, Universit\u00e0 di Padova, via Belzoni 7, 35131 Padova, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica Pura e Applicata, Universit\u00e0 di Padova, via Belzoni 7, 35131 Padova, Italy","institution_ids":["https://openalex.org/I138689650"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110938499","display_name":"Peter R. Wolenski","orcid":null},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peter R. Wolenski","raw_affiliation_strings":["Department of Mathematics, Louisiana State University, 326 Lockett Hall, Baton Rouge, LA 70803-4918"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Louisiana State University, 326 Lockett Hall, Baton Rouge, LA 70803-4918","institution_ids":["https://openalex.org/I121820613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9714,"has_fulltext":false,"cited_by_count":34,"citation_normalized_percentile":{"value":0.76008755,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"44","issue":"6","first_page":"2285","last_page":"2299"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10545","display_name":"Optimization and Variational Analysis","score":0.996999979019165,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.996999979019165,"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":0.996399998664856,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/epigraph","display_name":"Epigraph","score":0.9140223264694214},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8682162761688232},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6838631629943848},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.5686399340629578},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.5570112466812134},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5328508019447327},{"id":"https://openalex.org/keywords/radius","display_name":"RADIUS","score":0.5151951909065247},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.49212878942489624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47911834716796875},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43100547790527344},{"id":"https://openalex.org/keywords/continuous-function","display_name":"Continuous function (set theory)","score":0.42743220925331116},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19836804270744324}],"concepts":[{"id":"https://openalex.org/C17192189","wikidata":"https://www.wikidata.org/wiki/Q1347059","display_name":"Epigraph","level":2,"score":0.9140223264694214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8682162761688232},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6838631629943848},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.5686399340629578},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.5570112466812134},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5328508019447327},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.5151951909065247},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.49212878942489624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47911834716796875},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43100547790527344},{"id":"https://openalex.org/C2778199601","wikidata":"https://www.wikidata.org/wiki/Q5165476","display_name":"Continuous function (set theory)","level":3,"score":0.42743220925331116},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19836804270744324},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"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":3,"locations":[{"id":"doi:10.1137/050630076","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050630076","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:repository.lsu.edu:mathematics_pubs-2883","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/1881","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:www.research.unipd.it:11577/1561047","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/1561047","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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:www.research.unipd.it:11577/1561047","is_oa":true,"landing_page_url":"http://hdl.handle.net/11577/1561047","pdf_url":null,"source":{"id":"https://openalex.org/S4306402547","display_name":"Padua Research Archive (University of Padova)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I138689650","host_organization_name":"University of Padua","host_organization_lineage":["https://openalex.org/I138689650"],"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":24,"referenced_works":["https://openalex.org/W564809451","https://openalex.org/W1480714962","https://openalex.org/W1487586009","https://openalex.org/W1494380031","https://openalex.org/W1526586213","https://openalex.org/W1527244075","https://openalex.org/W1565973198","https://openalex.org/W1573659356","https://openalex.org/W1960239420","https://openalex.org/W1974468996","https://openalex.org/W1981285936","https://openalex.org/W2011909711","https://openalex.org/W2042138754","https://openalex.org/W2077522937","https://openalex.org/W2082575319","https://openalex.org/W2083001486","https://openalex.org/W2083111157","https://openalex.org/W2396132789","https://openalex.org/W2415568859","https://openalex.org/W2789131207","https://openalex.org/W3023757544","https://openalex.org/W4210718478","https://openalex.org/W4213171111","https://openalex.org/W4255677379"],"related_works":["https://openalex.org/W4246336996","https://openalex.org/W4385382439","https://openalex.org/W4229686360","https://openalex.org/W2417049975","https://openalex.org/W4238099065","https://openalex.org/W4310207256","https://openalex.org/W2405156719","https://openalex.org/W2376959945","https://openalex.org/W2800997595","https://openalex.org/W2411013118"],"abstract_inverted_index":{"A":[0],"minimal":[1,21],"time":[2,22],"problem":[3],"with":[4,36],"linear":[5],"dynamics":[6],"and":[7,54,72],"convex":[8],"target":[9],"is":[10,13,25,42],"considered.":[11],"It":[12],"shown,":[14],"essentially,":[15],"that":[16],"the":[17,20,76],"epigraph":[18],"of":[19,32,70,79],"function":[23],"$T(\\cdot)$":[24,41,71],"$\\varphi$-convex":[26],"(i.e.,":[27],"it":[28],"satisfies":[29],"a":[30],"kind":[31],"exterior":[33],"sphere":[34],"condition":[35],"locally":[37],"uniform":[38],"radius),":[39],"provided":[40],"continuous.":[43],"Several":[44],"regularity":[45],"properties":[46],"are":[47],"derived":[48],"from":[49],"results":[50],"in":[51],"[G.":[52],"Colombo":[53],"A.":[55],"Marigonda,":[56],"Calc.":[57],"Var.":[58],"Partial":[59],"Differential":[60],"Equations,":[61],"25":[62],"(2005),":[63],"pp.":[64],"1-31],":[65],"including":[66],"twice":[67],"a.e.":[68],"differentiability":[69],"local":[73],"estimates":[74],"on":[75],"total":[77],"variation":[78],"$DT$.":[80]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2025-10-10T00:00:00"}
