{"id":"https://openalex.org/W4407498564","doi":"https://doi.org/10.1515/ans-2023-0166","title":"Convergence rates of eigenvalue problems in perforated domains: the case of small volume","display_name":"Convergence rates of eigenvalue problems in perforated domains: the case of small volume","publication_year":2025,"publication_date":"2025-02-13","ids":{"openalex":"https://openalex.org/W4407498564","doi":"https://doi.org/10.1515/ans-2023-0166"},"language":"en","primary_location":{"id":"doi:10.1515/ans-2023-0166","doi":"https://doi.org/10.1515/ans-2023-0166","is_oa":true,"landing_page_url":"https://doi.org/10.1515/ans-2023-0166","pdf_url":null,"source":{"id":"https://openalex.org/S207995962","display_name":"Advanced Nonlinear Studies","issn_l":"1536-1365","issn":["1536-1365","2169-0375"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Nonlinear Studies","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1515/ans-2023-0166","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065781968","display_name":"Zhongwei Shen","orcid":"https://orcid.org/0000-0003-2387-7342","observed_orcids":["https://orcid.org/0000-0003-2387-7342"]},"institutions":[{"id":"https://openalex.org/I143302722","display_name":"University of Kentucky","ror":"https://ror.org/02k3smh20","country_code":"US","type":"education","lineage":["https://openalex.org/I143302722"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhongwei Shen","raw_affiliation_strings":["Department of Mathematics , University of Kentucky , Lexington , KY 40506 , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics , University of Kentucky , Lexington , KY 40506 , USA","institution_ids":["https://openalex.org/I143302722"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067745875","display_name":"Jinping Zhuge","orcid":"https://orcid.org/0000-0003-2661-4222","observed_orcids":["https://orcid.org/0000-0003-2661-4222"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinping Zhuge","raw_affiliation_strings":["Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences , Beijing , China","institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1300,"currency":"EUR","value_usd":1469},"apc_paid":{"value":1300,"currency":"EUR","value_usd":1469},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.05885488,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"25","issue":"2","first_page":"364","last_page":"408"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9829000234603882,"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"}},"topics":[{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9829000234603882,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.009399999864399433,"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":0.0038999998942017555,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/dirichlet-eigenvalues","display_name":"Dirichlet eigenvalues","score":0.9010000228881836},{"id":"https://openalex.org/keywords/laplacian","display_name":"Laplacian","score":0.8299999833106995},{"id":"https://openalex.org/keywords/periodic-perforations","display_name":"periodic perforations","score":0.8650000095367432},{"id":"https://openalex.org/keywords/small-volume","display_name":"small volume","score":0.7599999904632568},{"id":"https://openalex.org/keywords/convergence-rate","display_name":"convergence rate","score":0.8659999966621399},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"asymptotic expansion","score":0.843999981880188},{"id":"https://openalex.org/keywords/spectral-gap","display_name":"spectral gap","score":0.9229999780654907}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8751838207244873},{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.7473804950714111},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7383198738098145},{"id":"https://openalex.org/C102231394","wikidata":"https://www.wikidata.org/wiki/Q5280763","display_name":"Dirichlet eigenvalue","level":5,"score":0.7207764983177185},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6100034117698669},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5860955715179443},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5218181014060974},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.45359912514686584},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4530408978462219},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4512171745300293},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.44670096039772034},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4296107292175293},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4177592396736145},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.41555511951446533},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.41361361742019653},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.20726048946380615},{"id":"https://openalex.org/C148158259","wikidata":"https://www.wikidata.org/wiki/Q975727","display_name":"Dirichlet's principle","level":4,"score":0.15299060940742493},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1515/ans-2023-0166","doi":"https://doi.org/10.1515/ans-2023-0166","is_oa":true,"landing_page_url":"https://doi.org/10.1515/ans-2023-0166","pdf_url":null,"source":{"id":"https://openalex.org/S207995962","display_name":"Advanced Nonlinear Studies","issn_l":"1536-1365","issn":["1536-1365","2169-0375"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Nonlinear Studies","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2408.14278","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2408.14278","pdf_url":"https://arxiv.org/pdf/2408.14278","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:doaj.org/article:9e8d62adc21c46e1bc80e1d02232b5d7","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/9e8d62adc21c46e1bc80e1d02232b5d7","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,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Advanced Nonlinear Studies, Vol 25, Iss 2, Pp 364-408 (2025)","raw_type":"article"},{"id":"doi:10.48550/arxiv.2408.14278","doi":"https://doi.org/10.48550/arxiv.2408.14278","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2408.14278","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,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.1515/ans-2023-0166","doi":"https://doi.org/10.1515/ans-2023-0166","is_oa":true,"landing_page_url":"https://doi.org/10.1515/ans-2023-0166","pdf_url":null,"source":{"id":"https://openalex.org/S207995962","display_name":"Advanced Nonlinear Studies","issn_l":"1536-1365","issn":["1536-1365","2169-0375"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["anvur-scientific","cwts-core","doaj","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advanced Nonlinear Studies","raw_type":"journal-article"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W9352720","https://openalex.org/W2014618685","https://openalex.org/W2071539508","https://openalex.org/W2106902034","https://openalex.org/W2120554329","https://openalex.org/W2594511594","https://openalex.org/W2890378243","https://openalex.org/W2963085513","https://openalex.org/W3153491852","https://openalex.org/W4392365731","https://openalex.org/W4406832721"],"related_works":["https://openalex.org/W4302419125","https://openalex.org/W2766128145","https://openalex.org/W4300623652","https://openalex.org/W121031341","https://openalex.org/W2038878154","https://openalex.org/W4290982745","https://openalex.org/W2963746646","https://openalex.org/W2464780829","https://openalex.org/W3217737408","https://openalex.org/W2997119684"],"abstract_inverted_index":{"Abstract":[0],"This":[1],"paper":[2],"is":[3,76],"concerned":[4],"with":[5,17,42],"the":[6,21,28,35,52,56],"Dirichlet":[7,47],"eigenvalue":[8,69],"problem":[9,70],"for":[10,38,55,71],"Laplace":[11],"operator":[12],"in":[13,20],"a":[14,62,66,73],"bounded":[15],"domain":[16],"periodic":[18],"perforation":[19],"case":[22],"of":[23,34,46],"small":[24],"volume.":[25],"We":[26,49],"obtain":[27],"optimal":[29],"quantitative":[30,74],"error":[31],"estimates":[32],"independent":[33],"spectral":[36],"gaps":[37],"an":[39],"asymptotic":[40],"expansion,":[41],"two":[43],"leading":[44],"terms,":[45],"eigenvalues.":[48],"also":[50],"establish":[51],"convergence":[53],"rates":[54],"corresponding":[57],"eigenfunctions.":[58],"Our":[59],"approach":[60],"uses":[61],"known":[63],"reduction":[64],"to":[65],"degenerate":[67],"elliptic":[68],"which":[72],"analysis":[75],"carried":[77],"out.":[78]},"counts_by_year":[],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-02-14T00:00:00"}
