{"id":"https://openalex.org/W1444803443","doi":"https://doi.org/10.1007/0-387-23467-5_2","title":"Uniform Cusp Property, Boundary Integral, and Compactness for Shape Optimization","display_name":"Uniform Cusp Property, Boundary Integral, and Compactness for Shape Optimization","publication_year":2006,"publication_date":"2006-01-14","ids":{"openalex":"https://openalex.org/W1444803443","doi":"https://doi.org/10.1007/0-387-23467-5_2","mag":"1444803443"},"language":"en","primary_location":{"id":"doi:10.1007/0-387-23467-5_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-23467-5_2","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-23467-5_2.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/0-387-23467-5_2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5026288038","display_name":"Michel C. Delfour","orcid":"https://orcid.org/0000-0002-5642-2996"},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Michel C. Delfour","raw_affiliation_strings":["Centre de recherches math\u00e9matiques et D\u00e9partement de math\u00e9matiques et de statistique, Universit\u00e9 de Montreal, C.P. 6128, succ. Centre-ville, Montr\u00e9al, Qc, Canada, H3C 3J7"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre de recherches math\u00e9matiques et D\u00e9partement de math\u00e9matiques et de statistique, Universit\u00e9 de Montreal, C.P. 6128, succ. Centre-ville, Montr\u00e9al, Qc, Canada, H3C 3J7","institution_ids":["https://openalex.org/I70931966"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091048180","display_name":"Nicolas Doyon","orcid":null},"institutions":[{"id":"https://openalex.org/I70931966","display_name":"Universit\u00e9 de Montr\u00e9al","ror":"https://ror.org/0161xgx34","country_code":"CA","type":"education","lineage":["https://openalex.org/I70931966"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Nicolas Doyon","raw_affiliation_strings":["D\u00e9partement de math\u00e9matiques et de statistique, Universit\u00e9 de Montr\u00e9al, C. P. 6128, succ. Centre-ville, Montr\u00e9al, Qc, Canada, H3C 3J1"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"D\u00e9partement de math\u00e9matiques et de statistique, Universit\u00e9 de Montr\u00e9al, C. P. 6128, succ. Centre-ville, Montr\u00e9al, Qc, Canada, H3C 3J1","institution_ids":["https://openalex.org/I70931966"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111393023","display_name":"Jean-Paul Zol\u00e9sio","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Paul Zol\u00e9sio","raw_affiliation_strings":["CNRS and INRIA, 2004 route des lucioles, BP 93, FR-06902, Sophia Antipolis, France","CNRS/INRIA, Sophia Antipolis, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CNRS and INRIA, 2004 route des lucioles, BP 93, FR-06902, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"CNRS/INRIA, Sophia Antipolis, France","institution_ids":["https://openalex.org/I1326498283","https://openalex.org/I1294671590"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9835,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.87564009,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"25","last_page":"40"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10678","display_name":"Inflammatory mediators and NSAID effects","score":0.9180999994277954,"subfield":{"id":"https://openalex.org/subfields/2736","display_name":"Pharmacology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}},"topics":[{"id":"https://openalex.org/T10678","display_name":"Inflammatory mediators and NSAID effects","score":0.9180999994277954,"subfield":{"id":"https://openalex.org/subfields/2736","display_name":"Pharmacology"},"field":{"id":"https://openalex.org/fields/27","display_name":"Medicine"},"domain":{"id":"https://openalex.org/domains/4","display_name":"Health Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/cusp","display_name":"Cusp (singularity)","score":0.8522835373878479},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7767342329025269},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.6864476203918457},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.631792426109314},{"id":"https://openalex.org/keywords/monotone-polygon","display_name":"Monotone polygon","score":0.6153738498687744},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5976656675338745},{"id":"https://openalex.org/keywords/hausdorff-dimension","display_name":"Hausdorff dimension","score":0.4558800458908081},{"id":"https://openalex.org/keywords/hausdorff-space","display_name":"Hausdorff space","score":0.4442859888076782},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44131016731262207},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.34593385457992554},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32736876606941223},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2511019706726074}],"concepts":[{"id":"https://openalex.org/C2778400075","wikidata":"https://www.wikidata.org/wiki/Q655275","display_name":"Cusp (singularity)","level":2,"score":0.8522835373878479},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7767342329025269},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.6864476203918457},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.631792426109314},{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.6153738498687744},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5976656675338745},{"id":"https://openalex.org/C194198291","wikidata":"https://www.wikidata.org/wiki/Q565186","display_name":"Hausdorff dimension","level":2,"score":0.4558800458908081},{"id":"https://openalex.org/C191399826","wikidata":"https://www.wikidata.org/wiki/Q326908","display_name":"Hausdorff space","level":2,"score":0.4442859888076782},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44131016731262207},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.34593385457992554},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32736876606941223},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2511019706726074}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/0-387-23467-5_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-23467-5_2","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-23467-5_2.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/0-387-23467-5_2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/0-387-23467-5_2","pdf_url":"https://link.springer.com/content/pdf/10.1007/0-387-23467-5_2.pdf","source":{"id":"https://openalex.org/S4306463519","display_name":"Kluwer Academic Publishers eBooks","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"ebook platform"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IFIP International Federation for Information Processing","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321747","display_name":"Fonds Qu\u00e9b\u00e9cois de la Recherche sur la Nature et les Technologies","ror":"https://ror.org/00b9f9778"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1444803443.pdf","grobid_xml":"https://content.openalex.org/works/W1444803443.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W178344362","https://openalex.org/W616635904","https://openalex.org/W1489458628","https://openalex.org/W2018086174","https://openalex.org/W2047704663","https://openalex.org/W2481453809"],"related_works":["https://openalex.org/W2121543990","https://openalex.org/W2402800040","https://openalex.org/W2000020320","https://openalex.org/W4252969132","https://openalex.org/W1981078319","https://openalex.org/W2587346990","https://openalex.org/W4387315838","https://openalex.org/W2805799113","https://openalex.org/W2077709279","https://openalex.org/W2055388154"],"abstract_inverted_index":{"In":[0,29],"this":[1],"paper":[2],"we":[3,33,41],"consider":[4],"the":[5,10,27,30,54,75,91,108,128,133,160],"family":[6,109,158],"of":[7,53,63,74,94,110,112,136,162],"sets":[8],"verifying":[9,117,164],"uniform":[11,119,124,145,166],"cusp":[12,22,39,51,72,120],"property":[13,121],"introduced":[14,56],"in":[15,19,57,67],"[2]":[16],"and":[17,47,90,138],"extended":[18,38],"[4]":[20],"to":[21,36],"functions":[23],"only":[24],"continuous":[25],"at":[26],"origin.":[28],"latter":[31],"case":[32],"show":[34],"that":[35],"any":[37],"function,":[40],"can":[42],"associate":[43],"a":[44,64,71,113,118,123,155,165],"continuous,":[45],"non-negative,":[46],"monotone":[48],"strictly":[49],"increasing":[50],"function":[52,73],"type":[55],"[2].":[58],"We":[59,102,141],"construct":[60],"an":[61],"example":[62],"bounded":[65,114],"set":[66],"R":[68],"N":[69,99],"with":[70,122],"form":[76],"c|\u03b8|\u03b1,":[77],"0":[78],"<":[79,81],"\u03b1":[80],"1,":[82],"for":[83,107],"which":[84],"its":[85,95],"boundary":[86,96],"integral":[87],"is":[88,97],"infinite":[89],"Hausdorff":[92],"dimension":[93],"exactly":[98],"\u2212":[100],"\u03b1.":[101],"then":[103],"give":[104,143],"compactness":[105],"theorems":[106],"subsets":[111,163],"open":[115],"holdall":[116],"bound":[125],"on":[126],"either":[127],"De":[129],"Georgi":[130],"[6]":[131],"or":[132],"\u03b3-density":[134],"perimeter":[135],"Bucur":[137],"Zol\u00e9sio":[139],"[1].":[140],"also":[142],"their":[144],"local":[146],"C":[147],"0-graph":[148],"versions":[149],"following":[150],"[4].":[151],"This":[152],"class":[153],"forms":[154],"much":[156],"larger":[157],"than":[159],"one":[161],"cone":[167],"property.":[168]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
