{"id":"https://openalex.org/W2035690811","doi":"https://doi.org/10.1137/120869857","title":"Localization of Laplacian Eigenfunctions in Circular, Spherical, and Elliptical Domains","display_name":"Localization of Laplacian Eigenfunctions in Circular, Spherical, and Elliptical Domains","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2035690811","doi":"https://doi.org/10.1137/120869857","mag":"2035690811"},"language":"en","primary_location":{"id":"doi:10.1137/120869857","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120869857","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1203.5022","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047730752","display_name":"Binh-Thanh Nguyen","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":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"B.-T. Nguyen","raw_affiliation_strings":["Laboratoire de Physique de la Mati\u00e8re Condens\u00e9e, CNRS -Ecole Polytechnique, 91128 Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Physique de la Mati\u00e8re Condens\u00e9e, CNRS -Ecole Polytechnique, 91128 Palaiseau, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I142476485"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077899527","display_name":"Denis S. Grebenkov","orcid":"https://orcid.org/0000-0002-6273-9164"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I69295118","display_name":"Independent University of Moscow","ror":"https://ror.org/00ygzyy93","country_code":"RU","type":"education","lineage":["https://openalex.org/I69295118"]},{"id":"https://openalex.org/I172901346","display_name":"St Petersburg University","ror":"https://ror.org/023znxa73","country_code":"RU","type":"education","lineage":["https://openalex.org/I172901346"]},{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]}],"countries":["FR","RU"],"is_corresponding":true,"raw_author_name":"D. S. Grebenkov","raw_affiliation_strings":["Laboratoire Poncelet, CNRS -Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia","Laboratoire de Physique de la Mati\u00e8re Condens\u00e9e, CNRS -Ecole Polytechnique, 91128 Palaiseau, France","Chebyshev Laboratory, Saint Petersburg State University, 14th line of Vasil'evskiy Ostrov 29, Saint Petersburg, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Poncelet, CNRS -Independent University of Moscow, Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia","institution_ids":["https://openalex.org/I69295118"]},{"raw_affiliation_string":"Laboratoire de Physique de la Mati\u00e8re Condens\u00e9e, CNRS -Ecole Polytechnique, 91128 Palaiseau, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I142476485"]},{"raw_affiliation_string":"Chebyshev Laboratory, Saint Petersburg State University, 14th line of Vasil'evskiy Ostrov 29, Saint Petersburg, Russia","institution_ids":["https://openalex.org/I172901346"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5077899527"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I172901346","https://openalex.org/I69295118"],"apc_list":null,"apc_paid":null,"fwci":2.6072,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.89523357,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"73","issue":"2","first_page":"780","last_page":"803"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9926000237464905,"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":0.9926000237464905,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9900000095367432,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9869999885559082,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/eigenfunction","display_name":"Eigenfunction","score":0.8164368271827698},{"id":"https://openalex.org/keywords/bessel-function","display_name":"Bessel function","score":0.7162619829177856},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.6218950748443604},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.6070939302444458},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5916550159454346},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5640947222709656},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.559046745300293},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5110877156257629},{"id":"https://openalex.org/keywords/ball","display_name":"Ball (mathematics)","score":0.47397106885910034},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.46796613931655884},{"id":"https://openalex.org/keywords/annulus","display_name":"Annulus (botany)","score":0.4431880712509155},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3494286835193634},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3352503180503845},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2938392460346222},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.22525179386138916}],"concepts":[{"id":"https://openalex.org/C128803854","wikidata":"https://www.wikidata.org/wiki/Q1307821","display_name":"Eigenfunction","level":3,"score":0.8164368271827698},{"id":"https://openalex.org/C107706756","wikidata":"https://www.wikidata.org/wiki/Q219637","display_name":"Bessel function","level":2,"score":0.7162619829177856},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.6218950748443604},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.6070939302444458},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5916550159454346},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5640947222709656},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.559046745300293},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5110877156257629},{"id":"https://openalex.org/C122041747","wikidata":"https://www.wikidata.org/wiki/Q838611","display_name":"Ball (mathematics)","level":2,"score":0.47397106885910034},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.46796613931655884},{"id":"https://openalex.org/C150936888","wikidata":"https://www.wikidata.org/wiki/Q4769748","display_name":"Annulus (botany)","level":2,"score":0.4431880712509155},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3494286835193634},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3352503180503845},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2938392460346222},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.22525179386138916},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120869857","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120869857","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1203.5022","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.5022","pdf_url":"https://arxiv.org/pdf/1203.5022","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1203.5022","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1203.5022","pdf_url":"https://arxiv.org/pdf/1203.5022","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W135263833","https://openalex.org/W1503087463","https://openalex.org/W1723600880","https://openalex.org/W1964028571","https://openalex.org/W1967604287","https://openalex.org/W1970297574","https://openalex.org/W1974806351","https://openalex.org/W1983349998","https://openalex.org/W1987547729","https://openalex.org/W1992899169","https://openalex.org/W1997199842","https://openalex.org/W1998288323","https://openalex.org/W2016302698","https://openalex.org/W2023140343","https://openalex.org/W2026718533","https://openalex.org/W2030094057","https://openalex.org/W2036291650","https://openalex.org/W2047389283","https://openalex.org/W2058647411","https://openalex.org/W2064221873","https://openalex.org/W2076278340","https://openalex.org/W2080938048","https://openalex.org/W2082588476","https://openalex.org/W2083172865","https://openalex.org/W2086573468","https://openalex.org/W2087433201","https://openalex.org/W2090711173","https://openalex.org/W2111271529","https://openalex.org/W2144341414","https://openalex.org/W2145958836","https://openalex.org/W2147915021","https://openalex.org/W2322774782","https://openalex.org/W2327675911"],"related_works":["https://openalex.org/W3105576504","https://openalex.org/W2771721750","https://openalex.org/W4294620502","https://openalex.org/W3047312258","https://openalex.org/W2183371396","https://openalex.org/W4302419125","https://openalex.org/W2766128145","https://openalex.org/W4300623652","https://openalex.org/W121031341","https://openalex.org/W2038878154"],"abstract_inverted_index":{"We":[0],"consider":[1],"Laplacian":[2],"eigenfunctions":[3],"in":[4,10,69,131,146,152],"circular,":[5,48],"spherical,":[6,49],"and":[7,25,50,76,87,95],"elliptical":[8,51,109],"domains":[9,52,148],"order":[11],"to":[12,55,139],"discuss":[13],"three":[14],"kinds":[15],"of":[16,31,40,45,60,73,85,104,144],"high-frequency":[17,114],"localization:":[18],"whispering":[19],"gallery":[20],"modes,":[21,24],"bouncing":[22],"ball":[23],"focusing":[26],"modes.":[27],"Although":[28],"the":[29,43,58,74,83,113,121],"existence":[30],"these":[32],"modes":[33,116],"has":[34],"been":[35],"known":[36],"for":[37,47,111],"a":[38,70,105],"class":[39],"convex":[41,155],"domains,":[42],"separation":[44],"variables":[46],"helps":[53],"us":[54,138],"better":[56],"understand":[57],"\u201cmechanism\u201d":[59],"localization,":[61],"i.e.,":[62],"how":[63],"an":[64,102,141],"eigenfunction":[65],"is":[66,128],"getting":[67],"distributed":[68],"small":[71],"region":[72],"domain":[75,107],"decays":[77],"rapidly":[78],"outside":[79],"this":[80],"region.":[81],"Using":[82],"properties":[84],"Bessel":[86],"Mathieu":[88],"functions,":[89],"we":[90,100,124],"derive":[91],"inequalities":[92],"which":[93,112],"imply":[94],"clearly":[96],"illustrate":[97],"localization.":[98],"Moreover,":[99],"provide":[101],"example":[103],"nonconvex":[106],"(an":[108],"annulus)":[110],"localized":[115],"are":[117],"still":[118],"present.":[119],"At":[120],"same":[122],"time,":[123],"show":[125],"that":[126],"there":[127],"no":[129],"localization":[130,145],"most":[132],"rectangle-like":[133],"domains.":[134,156],"This":[135],"observation":[136],"leads":[137],"formulate":[140],"open":[142],"problem":[143],"polygonal":[147],"and,":[149],"more":[150],"generally,":[151],"piecewise":[153],"smooth":[154]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}
