{"id":"https://openalex.org/W2989420777","doi":"https://doi.org/10.1137/18m1223927","title":"Continuum Limits of Nonlocal $p$-Laplacian Variational Problems on Graphs","display_name":"Continuum Limits of Nonlocal $p$-Laplacian Variational Problems on Graphs","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2989420777","doi":"https://doi.org/10.1137/18m1223927","mag":"2989420777"},"language":"en","primary_location":{"id":"doi:10.1137/18m1223927","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1223927","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-02268163/document","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055793444","display_name":"Yosra Hafiene","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yosra Hafiene","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008136365","display_name":"Jalal Fadili","orcid":"https://orcid.org/0000-0002-8165-7578"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jalal M. Fadili","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5068967480","display_name":"Abderrahim Elmoataz","orcid":"https://orcid.org/0000-0001-7762-5269"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Abderrahim Elmoataz","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":0.6451,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.67321692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":"12","issue":"4","first_page":"1772","last_page":"1807"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.23360000550746918,"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":0.23360000550746918,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.19300000369548798,"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"}},{"id":"https://openalex.org/T11347","display_name":"Neural Networks Stability and Synchronization","score":0.07519999891519547,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/mathematics","display_name":"Mathematics","score":0.7272015810012817},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5637584328651428},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5627444386482239},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.4511031210422516},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4491382837295532},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4272254407405853},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.31339865922927856},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28799718618392944},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25848352909088135},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10642784833908081}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7272015810012817},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5637584328651428},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5627444386482239},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.4511031210422516},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4491382837295532},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4272254407405853},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.31339865922927856},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28799718618392944},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25848352909088135},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10642784833908081},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m1223927","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1223927","pdf_url":null,"source":{"id":"https://openalex.org/S152600803","display_name":"SIAM Journal on Imaging Sciences","issn_l":"1936-4954","issn":["1936-4954"],"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 Imaging Sciences","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-02268163v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02268163","pdf_url":"https://hal.science/hal-02268163/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Imaging Sciences, 2019","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-02268163v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02268163","pdf_url":"https://hal.science/hal-02268163/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Imaging Sciences, 2019","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320322893","display_name":"Institut Universitaire de France","ror":"https://ror.org/055khg266"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2989420777.pdf","grobid_xml":"https://content.openalex.org/works/W2989420777.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W322738573","https://openalex.org/W1511118377","https://openalex.org/W1826824261","https://openalex.org/W1837565340","https://openalex.org/W1861295442","https://openalex.org/W1976688370","https://openalex.org/W1984032850","https://openalex.org/W1991217933","https://openalex.org/W2002276939","https://openalex.org/W2006554089","https://openalex.org/W2007680066","https://openalex.org/W2019248995","https://openalex.org/W2025779824","https://openalex.org/W2038649727","https://openalex.org/W2060945009","https://openalex.org/W2082734581","https://openalex.org/W2099046646","https://openalex.org/W2099244020","https://openalex.org/W2100556411","https://openalex.org/W2132914434","https://openalex.org/W2136396015","https://openalex.org/W2136674316","https://openalex.org/W2147825506","https://openalex.org/W2149695599","https://openalex.org/W2320596590","https://openalex.org/W2577840663","https://openalex.org/W2962701197","https://openalex.org/W2963530915","https://openalex.org/W4213367101"],"related_works":["https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W1971388572","https://openalex.org/W3126543146","https://openalex.org/W2519362558","https://openalex.org/W3159754125","https://openalex.org/W58770712"],"abstract_inverted_index":{"In":[0,34],"this":[1,48,90],"paper,":[2],"we":[3,36,63,132],"study":[4,37],"a":[5,18,23,44],"nonlocal":[6,32,49,81],"variational":[7,50,86,102],"problem":[8,51,103,152],"which":[9],"consists":[10],"of":[11,17,30,39,47,56,72,99,107,138,140,149,156],"minimizing":[12],"in":[13,116],"$L^2$":[14],"the":[15,28,31,40,53,57,70,73,77,80,97,100,105,143,147,150,154],"sum":[16],"quadratic":[19],"data":[20,75],"fidelity":[21],"and":[22,68,76,121,135],"regularization":[24],"term":[25],"corresponding":[26],"to":[27,43,52,85,95,110,146],"$L^p$-norm":[29],"gradient.":[33],"particular,":[35],"convergence":[38,134,139],"numerical":[41],"solution":[42,55,148],"discrete":[45,144],"version":[46],"unique":[54],"continuum":[58,151],"one.":[59],"To":[60],"do":[61],"so,":[62],"derive":[64],"an":[65],"error":[66,91],"bound":[67,92],"highlight":[69],"role":[71],"initial":[74],"kernel":[78],"governing":[79],"interactions.":[82],"When":[83],"applied":[84],"problems":[87],"on":[88],"graphs,":[89],"allows":[93],"us":[94],"show":[96],"consistency":[98],"discretized":[101],"as":[104,126,128,153],"number":[106,155],"vertices":[108,157],"goes":[109],"infinity.":[111],"More":[112],"precisely,":[113],"for":[114,142],"networks":[115],"convergent":[117],"graph":[118],"sequences":[119],"(simple":[120],"weighted":[122],"deterministic":[123],"dense":[124],"graphs":[125],"well":[127],"random":[129],"inhomogeneous":[130],"graphs),":[131],"prove":[133],"provide":[136],"rates":[137],"solutions":[141],"models":[145],"grows.":[158]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
