{"id":"https://openalex.org/W1720750060","doi":"https://doi.org/10.3233/asy-2011-1042","title":"On a homogenization technique for singular integrals","display_name":"On a homogenization technique for singular integrals","publication_year":2011,"publication_date":"2011-09-01","ids":{"openalex":"https://openalex.org/W1720750060","doi":"https://doi.org/10.3233/asy-2011-1042","mag":"1720750060"},"language":"en","primary_location":{"id":"doi:10.3233/asy-2011-1042","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2011-1042","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-00797473","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010666405","display_name":"Omar Anza Hafsa","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/I19894307","display_name":"Universit\u00e9 de Montpellier","ror":"https://ror.org/051escj72","country_code":"FR","type":"education","lineage":["https://openalex.org/I19894307"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Omar Anza Hafsa","raw_affiliation_strings":["Universite Montpellier II, UMR-CNRS 5508, LMGC, Place Eug\u00e8ne Bataillon, 34095 Montpellier, France E-mail: Omar.Anza-Hafsa@univ-montp2.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universite Montpellier II, UMR-CNRS 5508, LMGC, Place Eug\u00e8ne Bataillon, 34095 Montpellier, France E-mail: Omar.Anza-Hafsa@univ-montp2.fr","institution_ids":["https://openalex.org/I19894307","https://openalex.org/I1294671590"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083602865","display_name":"Mohamed Lamine Leghmizi","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128965","display_name":"University Yahia Fares of Medea","ror":"https://ror.org/02e2yc259","country_code":"DZ","type":"education","lineage":["https://openalex.org/I4210128965"]}],"countries":["DZ"],"is_corresponding":false,"raw_author_name":"Mohamed Lamine Leghmizi","raw_affiliation_strings":["Laboratoire de M\u00e9canique, Physique et Mod\u00e9lisation Math\u00e9matique, Universite de M\u00e9d\u00e9a, LMP2M, Quartier Ain-D'Heb, M\u00e9d\u00e9a 26000, Algerie. E-mail: leghmizi@hotmail.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de M\u00e9canique, Physique et Mod\u00e9lisation Math\u00e9matique, Universite de M\u00e9d\u00e9a, LMP2M, Quartier Ain-D'Heb, M\u00e9d\u00e9a 26000, Algerie. E-mail: leghmizi@hotmail.com","institution_ids":["https://openalex.org/I4210128965"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5073130063","display_name":"Jean-Philippe Mandallena","orcid":null},"institutions":[{"id":"https://openalex.org/I66456633","display_name":"Universit\u00e9 de N\u00eemes","ror":"https://ror.org/044t4x544","country_code":"FR","type":"education","lineage":["https://openalex.org/I66456633"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Jean-Philippe Mandallena","raw_affiliation_strings":["Laboratoire MIPA, Universite de N\u00eemes, Site des Carmes, Place Gabriel P\u00e9ri, 30021 N\u00eemes, France. E-mail: jean-philippe.mandallena@unimes.fr"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire MIPA, Universite de N\u00eemes, Site des Carmes, Place Gabriel P\u00e9ri, 30021 N\u00eemes, France. E-mail: jean-philippe.mandallena@unimes.fr","institution_ids":["https://openalex.org/I66456633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5010666405"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I19894307"],"apc_list":null,"apc_paid":null,"fwci":0.3261,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.57494415,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"74","issue":"3-4","first_page":"123","last_page":"134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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/T11558","display_name":"Composite Material Mechanics","score":0.987500011920929,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9854000210762024,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/homogenization","display_name":"Homogenization (climate)","score":0.9386341571807861},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6913262009620667},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6422206163406372},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4729851484298706},{"id":"https://openalex.org/keywords/open-set","display_name":"Open set","score":0.4275054931640625},{"id":"https://openalex.org/keywords/singular-integral","display_name":"Singular integral","score":0.42201468348503113},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.35941994190216064},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.05711612105369568}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.9386341571807861},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6913262009620667},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6422206163406372},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4729851484298706},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.4275054931640625},{"id":"https://openalex.org/C92571104","wikidata":"https://www.wikidata.org/wiki/Q888122","display_name":"Singular integral","level":3,"score":0.42201468348503113},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.35941994190216064},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.05711612105369568},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3233/asy-2011-1042","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2011-1042","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.400.4275","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.400.4275","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://hal.archives-ouvertes.fr/docs/00/79/74/73/PDF/On_homogenization_technique_Anza-Hafsa_al.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00797473v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00797473","pdf_url":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Asymptotic Analysis, 2011, 74 (3-4), pp.123-134. ⟨10.3233/ASY-2011-1042⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00797473v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00797473","pdf_url":null,"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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Asymptotic Analysis, 2011, 74 (3-4), pp.123-134. ⟨10.3233/ASY-2011-1042⟩","raw_type":"Journal articles"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W49749079","https://openalex.org/W91114896","https://openalex.org/W656727543","https://openalex.org/W1499205335","https://openalex.org/W1537639429","https://openalex.org/W1581406479","https://openalex.org/W1604436244","https://openalex.org/W1662321012","https://openalex.org/W2014133061","https://openalex.org/W2014212235","https://openalex.org/W2016444418","https://openalex.org/W2017364303","https://openalex.org/W2023516084","https://openalex.org/W2030708210","https://openalex.org/W2059450582","https://openalex.org/W2167868331","https://openalex.org/W2475471699","https://openalex.org/W2949235778","https://openalex.org/W4252823740"],"related_works":["https://openalex.org/W2104620528","https://openalex.org/W140119233","https://openalex.org/W2757910772","https://openalex.org/W4249473811","https://openalex.org/W2394422079","https://openalex.org/W2025913943","https://openalex.org/W2026826484","https://openalex.org/W945412790","https://openalex.org/W4388323431","https://openalex.org/W4243277272"],"abstract_inverted_index":{"We":[0],"study":[1],"homogenization":[2,44],"by":[3],"\u0393-convergence":[4],"of":[5,7,40,57],"functionals":[6],"type":[8,58],"\u222b":[9],"\u03a9":[10],"W(x/\u03b5,\u2207\u03d5(x))":[11],"dx,":[12],"where":[13],"Omega\u2282R":[14],"N":[15,34],"is":[16,38,66],"a":[17,54],"bounded":[18],"open":[19],"set,":[20],"\u03d5\u2208W":[21],"1,p":[22],"(Omega;R":[23],"m":[24],")":[25],"and":[26,51,74],"p>1,":[27],"when":[28,49],"the":[29,70],"1-periodic":[30],"integrand":[31],"W":[32,52],":R":[33],"\u00d7M":[35],"m\u00d7N":[36],"\u2192[0,+\u221e]":[37],"not":[39,67],"p-polynomial":[41],"growth.":[42],"Our":[43],"technique":[45,65],"can":[46],"be":[47],"applied":[48],"m=N":[50],"has":[53],"singular":[55],"behavior":[56],"W(x,\u03be)\u2192+\u221e":[59],"as":[60],"det":[61,77],"\u03be\u21920.":[62],"However,":[63],"our":[64],"consistent":[68],"with":[69],"constraint":[71],"W(x,\u03be)=+\u221e":[72],"if":[73,76],"only":[75],"\u03be\u22640.":[78]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}