{"id":"https://openalex.org/W3170122327","doi":"https://doi.org/10.3934/nhm.2021019","title":"Convex and quasiconvex functions in metric graphs","display_name":"Convex and quasiconvex functions in metric graphs","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3170122327","doi":"https://doi.org/10.3934/nhm.2021019","mag":"3170122327"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2021019","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021019","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=4af364ae-e8fd-428c-8aae-faea4a8103cd","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.aimsciences.org/article/exportPdf?id=4af364ae-e8fd-428c-8aae-faea4a8103cd","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041065153","display_name":"Leandro M. Del Pezzo","orcid":"https://orcid.org/0000-0002-5263-3446"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Leandro M. Del Pezzo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021209269","display_name":"Nicol\u00e1s Frevenza","orcid":"https://orcid.org/0000-0002-6002-6785"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nicol\u00e1s Frevenza","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5107115488","display_name":"Julio D. Rossi","orcid":"https://orcid.org/0000-0001-7622-2759"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Julio D. Rossi","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":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11763958,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"16","issue":"4","first_page":"591","last_page":"591"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9976000189781189,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9976000189781189,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9866999983787537,"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9775000214576721,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/quasiconvex-function","display_name":"Quasiconvex function","score":0.9894006252288818},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.730003833770752},{"id":"https://openalex.org/keywords/convex-function","display_name":"Convex function","score":0.49979138374328613},{"id":"https://openalex.org/keywords/convex-set","display_name":"Convex set","score":0.4717700779438019},{"id":"https://openalex.org/keywords/pseudoconvex-function","display_name":"Pseudoconvex function","score":0.45304396748542786},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.4430544078350067},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4349025785923004},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3735352158546448},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.32102417945861816},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.2441788613796234},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08805322647094727}],"concepts":[{"id":"https://openalex.org/C80278974","wikidata":"https://www.wikidata.org/wiki/Q1126412","display_name":"Quasiconvex function","level":5,"score":0.9894006252288818},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.730003833770752},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.49979138374328613},{"id":"https://openalex.org/C49870271","wikidata":"https://www.wikidata.org/wiki/Q193657","display_name":"Convex set","level":4,"score":0.4717700779438019},{"id":"https://openalex.org/C118888059","wikidata":"https://www.wikidata.org/wiki/Q7254692","display_name":"Pseudoconvex function","level":5,"score":0.45304396748542786},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.4430544078350067},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4349025785923004},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3735352158546448},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.32102417945861816},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.2441788613796234},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08805322647094727}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.3934/nhm.2021019","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021019","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=4af364ae-e8fd-428c-8aae-faea4a8103cd","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.14718","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.14718","pdf_url":"https://arxiv.org/pdf/2011.14718","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3170122327","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2011.14718","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:doaj.org/article:e941f2f4989d4beabc27f781a372b2b1","is_oa":false,"landing_page_url":"https://doaj.org/article/e941f2f4989d4beabc27f781a372b2b1","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 16, Iss 4, Pp 591-607 (2021)","raw_type":"article"},{"id":"pmh:oai:ri.conicet.gov.ar:11336/161929","is_oa":true,"landing_page_url":"http://hdl.handle.net/11336/161929","pdf_url":null,"source":{"id":"https://openalex.org/S4306401400","display_name":"Conicet","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210104196","host_organization_name":"Centro Cient\u00edfico Tecnol\u00f3gico - Nordeste","host_organization_lineage":["https://openalex.org/I4210104196"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2011.14718","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.14718","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.3934/nhm.2021019","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2021019","pdf_url":"https://www.aimsciences.org/article/exportPdf?id=4af364ae-e8fd-428c-8aae-faea4a8103cd","source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks & Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2083152754","display_name":"Problemas limites en ecuaciones diferenciales","funder_award_id":"11220150100036CO","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G4145340230","display_name":null,"funder_award_id":"PICT-2018-03183","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G5344391199","display_name":null,"funder_award_id":"PICT2018","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G5971969336","display_name":null,"funder_award_id":"20020160100155BA","funder_id":"https://openalex.org/F4320335478","funder_display_name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad de Buenos Aires"},{"id":"https://openalex.org/G7081472554","display_name":null,"funder_award_id":"PIP GI No 11220150100036CO","funder_id":"https://openalex.org/F4320321594","funder_display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas"},{"id":"https://openalex.org/G8310656700","display_name":null,"funder_award_id":"MTM2015-70227-P","funder_id":"https://openalex.org/F4320335478","funder_display_name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad de Buenos Aires"}],"funders":[{"id":"https://openalex.org/F4320321594","display_name":"Consejo Nacional de Investigaciones Cient\u00edficas y T\u00e9cnicas","ror":"https://ror.org/03cqe8w59"},{"id":"https://openalex.org/F4320335478","display_name":"Secretar\u00eda de Ciencia y T\u00e9cnica, Universidad de Buenos Aires","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3170122327.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W50901504","https://openalex.org/W135130007","https://openalex.org/W260353304","https://openalex.org/W402113276","https://openalex.org/W1531229952","https://openalex.org/W1984802537","https://openalex.org/W1985077192","https://openalex.org/W1996471450","https://openalex.org/W2014130083","https://openalex.org/W2061114984","https://openalex.org/W2080134189","https://openalex.org/W2081462933","https://openalex.org/W2102639652","https://openalex.org/W2115336412","https://openalex.org/W2160086716","https://openalex.org/W2168346106","https://openalex.org/W2304678994","https://openalex.org/W2562852663","https://openalex.org/W2594256465","https://openalex.org/W2744961039","https://openalex.org/W2935765814","https://openalex.org/W2962701685","https://openalex.org/W2963433336","https://openalex.org/W4206054140","https://openalex.org/W4292070096","https://openalex.org/W4297069203","https://openalex.org/W4312324038"],"related_works":["https://openalex.org/W3106804050","https://openalex.org/W2608069204","https://openalex.org/W3035769413","https://openalex.org/W15852313","https://openalex.org/W2549888807","https://openalex.org/W975017257","https://openalex.org/W2012800560","https://openalex.org/W1994727353","https://openalex.org/W2030892469","https://openalex.org/W2030895159","https://openalex.org/W2047402789","https://openalex.org/W2369632783","https://openalex.org/W1969949455","https://openalex.org/W2032277136","https://openalex.org/W2963600032","https://openalex.org/W166950480","https://openalex.org/W1557678201","https://openalex.org/W331269808","https://openalex.org/W2952361520","https://openalex.org/W2076829884"],"abstract_inverted_index":{"We":[0,29,61],"study":[1,63],"convex":[2,23,33],"and":[3,70],"quasiconvex":[4,68,77],"functions":[5,69],"on":[6,51],"a":[7,11,42,72,82],"metric":[8,17],"graph.":[9],"Given":[10],"set":[12],"of":[13,74],"points":[14],"in":[15],"the":[16,21,26,36,52,59,64,75],"graph,":[18],"we":[19],"consider":[20],"largest":[22,32,38,76],"function":[24,34,78],"below":[25,81],"prescribed":[27],"datum.":[28,84],"characterize":[30],"this":[31],"as":[35],"unique":[37],"viscosity":[39],"subsolution":[40],"to":[41],"simple":[43],"differential":[44],"equation,":[45],"\\begin{document}$":[46],"u''":[47],"=":[48],"0":[49],"$\\end{document}":[50],"edges,":[53],"plus":[54],"nonlinear":[55],"transmission":[56],"conditions":[57],"at":[58],"vertices.":[60],"also":[62],"analogous":[65],"problem":[66],"for":[67],"obtain":[71],"characterization":[73],"that":[79],"is":[80],"given":[83]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}