{"id":"https://openalex.org/W7220737590","doi":"https://doi.org/10.48550/arxiv.2610.05257","title":"Nontrivial periodic solutions to the one-phase free boundary problem","display_name":"Nontrivial periodic solutions to the one-phase free boundary problem","publication_year":2026,"publication_date":"2026-10-04","ids":{"openalex":"https://openalex.org/W7220737590","doi":"https://doi.org/10.48550/arxiv.2610.05257"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.05257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05257","pdf_url":"https://arxiv.org/pdf/2610.05257","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2610.05257","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5093299745","display_name":"Jos\u00e9 Basulto","orcid":"https://orcid.org/0009-0003-1772-2288","observed_orcids":["https://orcid.org/0009-0003-1772-2288"]},"institutions":[{"id":"https://openalex.org/I162148367","display_name":"Pontificia Universidad Cat\u00f3lica de Chile","ror":"https://ror.org/04teye511","country_code":"CL","type":"education","lineage":["https://openalex.org/I162148367"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Basulto, Jos\u00e9","raw_affiliation_strings":["Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago 7820436 , Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago 7820436 , Chile","institution_ids":["https://openalex.org/I162148367"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005948652","display_name":"Nikola Kamburov","orcid":"https://orcid.org/0000-0003-4998-3530","observed_orcids":["https://orcid.org/0000-0003-4998-3530"]},"institutions":[{"id":"https://openalex.org/I162148367","display_name":"Pontificia Universidad Cat\u00f3lica de Chile","ror":"https://ror.org/04teye511","country_code":"CL","type":"education","lineage":["https://openalex.org/I162148367"]}],"countries":["CL"],"is_corresponding":false,"raw_author_name":"Kamburov, Nikola","raw_affiliation_strings":["Nikola Kamburov , Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago 7820436 , Chile"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nikola Kamburov , Facultad de Matem\u00e1ticas , Pontificia Universidad Cat\u00f3lica de Chile , Avenida Vicu\u00f1a Mackenna 4860 , Santiago 7820436 , Chile","institution_ids":["https://openalex.org/I162148367"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I162148367"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.6952999830245972,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.6952999830245972,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.2915000021457672,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/one-phase-free-boundary-problem","display_name":"one-phase free boundary problem","score":0.8690000176429749},{"id":"https://openalex.org/keywords/periodic-solutions","display_name":"periodic solutions","score":0.8889999985694885},{"id":"https://openalex.org/keywords/bifurcation","display_name":"bifurcation","score":0.6499999761581421},{"id":"https://openalex.org/keywords/nondegeneracy","display_name":"nondegeneracy","score":0.7929999828338623},{"id":"https://openalex.org/keywords/product-solutions","display_name":"product solutions","score":0.421999990940094}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7520999908447266},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5698000192642212},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5087000131607056},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.4862000048160553},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.48019999265670776},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4366999864578247},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.4311000108718872},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.42250001430511475},{"id":"https://openalex.org/C140031139","wikidata":"https://www.wikidata.org/wiki/Q79897","display_name":"Morse code","level":2,"score":0.4117000102996826},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.374099999666214},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.34790000319480896},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.34040001034736633},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.3343000113964081},{"id":"https://openalex.org/C197617374","wikidata":"https://www.wikidata.org/wiki/Q755991","display_name":"Atiyah\u2013Singer index theorem","level":2,"score":0.3276999890804291},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C156730297","wikidata":"https://www.wikidata.org/wiki/Q2296951","display_name":"Morse theory","level":2,"score":0.27880001068115234},{"id":"https://openalex.org/C152361515","wikidata":"https://www.wikidata.org/wiki/Q181328","display_name":"Bernoulli's principle","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.25619998574256897}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.05257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05257","pdf_url":"https://arxiv.org/pdf/2610.05257","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2610.05257","doi":"https://doi.org/10.48550/arxiv.2610.05257","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.05257","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.05257","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.05257","pdf_url":"https://arxiv.org/pdf/2610.05257","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G562469049","display_name":"STABILITY IN FAMILIES OF FREE BOUNDARY INTERFACES","funder_award_id":"1241588","funder_id":"https://openalex.org/F4320331146","funder_display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo"}],"funders":[{"id":"https://openalex.org/F4320331146","display_name":"Agencia Nacional de Investigaci\u00f3n y Desarrollo","ror":"https://ror.org/05btm5233"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7220737590.pdf","grobid_xml":"https://content.openalex.org/works/W7220737590.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4224434603","https://openalex.org/W2982675636","https://openalex.org/W4392310924","https://openalex.org/W2984120828","https://openalex.org/W7160856392","https://openalex.org/W2616916747","https://openalex.org/W225970500","https://openalex.org/W570776761","https://openalex.org/W3147719007","https://openalex.org/W2798642573"],"abstract_inverted_index":{"We":[0],"construct":[1],"new":[2],"classical":[3],"global":[4],"solutions":[5,63,72,115,135,161,170],"of":[6,21,24,38,44,111,133,150],"the":[7,22,25,41,45,58,75,102,108,131,151,159],"one-phase":[8],"Bernoulli":[9],"free":[10,42,173],"boundary":[11,43,174],"problem":[12],"in":[13,64,136],"$\\mathbb{R}^3$":[14],"whose":[15],"positive":[16],"phases":[17],"are":[18,162],"periodic":[19,62],"perturbations":[20],"product":[23,71],"Hauswirth--H\u00e9lein--Pacard":[26],"double":[27],"hairpin":[28],"domain":[29],"with":[30,35,171],"a":[31,87,147,176],"line.":[32],"In":[33,98,154],"contrast":[34],"previous":[36],"constructions":[37],"undulating":[39,134],"cylinders,":[40],"base":[46,76,152],"solution":[47,125],"is":[48,84,106],"not":[49],"compact":[50],"modulo":[51],"translations.":[52],"More":[53],"generally,":[54],"we":[55,164],"show":[56],"that":[57,122,158,166],"same":[59],"scheme":[60],"yields":[61],"$\\mathbb{R}^{n+1}$,":[65],"$n":[66],"\\geq":[67],"3$,":[68],"bifurcating":[69,140],"from":[70,141],"$U(x,t)=u(x)$,":[73],"when":[74],"$u:\\mathbb{R}^n\\to":[77],"[0,\\infty)$":[78],"has":[79],"nontrivial":[80],"finite":[81,112,167],"Morse":[82,113,168],"index,":[83],"nondegenerate":[85],"within":[86],"symmetry":[88],"class,":[89],"and":[90,119,138],"satisfies":[91,126],"certain":[92],"natural":[93],"geometric":[94,128],"conditions":[95],"at":[96],"infinity.":[97],"dimensions":[99],"$n\\in\\{3,4\\}$,":[100],"where":[101],"stable":[103],"Bernstein":[104],"theorem":[105],"available,":[107],"recent":[109],"classification":[110],"index":[114,169],"by":[116],"Fern\u00e1ndez-Real,":[117],"Florit-Simon":[118],"Serra":[120],"shows":[121],"every":[123],"such":[124],"these":[127],"conditions.":[129],"Thus,":[130],"existence":[132],"$\\mathbb{R}^{4}$":[137],"$\\mathbb{R}^{5}$":[139],"their":[142],"respective":[143],"products":[144],"reduces":[145],"to":[146,156],"nondegeneracy":[148,179],"property":[149],"solution.":[153],"order":[155],"confirm":[157],"perturbed":[160],"positive,":[163],"prove":[165],"noncompact":[172],"satisfy":[175],"strong":[177],"distance":[178],"estimate.":[180]},"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2026-10-07T00:00:00"}