{"id":"https://openalex.org/W7206201902","doi":"https://doi.org/10.48550/arxiv.2609.01531","title":"Failure of Interior H\u00f6lder and Gradient Estimates for the Subcritical Special Lagrangian Equation","display_name":"Failure of Interior H\u00f6lder and Gradient Estimates for the Subcritical Special Lagrangian Equation","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7206201902","doi":"https://doi.org/10.48550/arxiv.2609.01531"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01531","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01531","pdf_url":"https://arxiv.org/pdf/2609.01531","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.01531","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101948577","display_name":"Zhenyu Fan","orcid":"https://orcid.org/0000-0002-6713-6514","observed_orcids":["https://orcid.org/0000-0002-6713-6514"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fan, Zhenyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5149351275","display_name":"Caiyan Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Caiyan","raw_affiliation_strings":["School of Mathematical Sciences , Xiamen University , Xiamen 361005 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences , Xiamen University , Xiamen 361005 , China","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5149198403","display_name":"Zhehui Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4396570619","display_name":"Great Bay University","ror":"https://ror.org/01hdgge16","country_code":"CN","type":"education","lineage":["https://openalex.org/I4396570619"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Zhehui","raw_affiliation_strings":["School of Sciences , Great Bay University , Dongguan 523000 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Sciences , Great Bay University , Dongguan 523000 , China","institution_ids":["https://openalex.org/I4396570619"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.6592000126838684,"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":0.6592000126838684,"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":0.3156999945640564,"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/T12351","display_name":"Geometry and complex manifolds","score":0.004900000058114529,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/special-lagrangian-equation","display_name":"special Lagrangian equation","score":0.9929999709129333},{"id":"https://openalex.org/keywords/subcritical-phase","display_name":"subcritical phase","score":0.8679999709129333},{"id":"https://openalex.org/keywords/holder-estimates","display_name":"H\u00f6lder estimates","score":0.7829999923706055},{"id":"https://openalex.org/keywords/modulus-of-continuity","display_name":"modulus of continuity","score":0.871999979019165},{"id":"https://openalex.org/keywords/real-analytic-solutions","display_name":"real analytic solutions","score":0.8230000138282776},{"id":"https://openalex.org/keywords/entire-solutions","display_name":"entire solutions","score":0.6850000023841858},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.5709999799728394}],"concepts":[{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.5302000045776367},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5260000228881836},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4846000075340271},{"id":"https://openalex.org/C44280652","wikidata":"https://www.wikidata.org/wiki/Q104837","display_name":"Phase (matter)","level":2,"score":0.40450000762939453},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.35910001397132874},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35350000858306885},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2976999878883362},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C193867417","wikidata":"https://www.wikidata.org/wiki/Q6889814","display_name":"Modulus","level":2,"score":0.2581000030040741},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.2402999997138977}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01531","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01531","pdf_url":"https://arxiv.org/pdf/2609.01531","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.2609.01531","doi":"https://doi.org/10.48550/arxiv.2609.01531","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01531","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:2609.01531","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01531","pdf_url":"https://arxiv.org/pdf/2609.01531","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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7206201902.pdf","grobid_xml":"https://content.openalex.org/works/W7206201902.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7216378723","https://openalex.org/W2061885154","https://openalex.org/W2085360607","https://openalex.org/W2079865956","https://openalex.org/W4406072733","https://openalex.org/W2947015531","https://openalex.org/W2947166906","https://openalex.org/W4206920124","https://openalex.org/W3213620066","https://openalex.org/W2948201513"],"abstract_inverted_index":{"For":[0],"every":[1,15,19],"$n\\ge3$,":[2],"we":[3],"show,":[4],"by":[5],"a":[6],"family":[7,36],"of":[8,42],"explicit":[9],"entire":[10],"real-analytic":[11],"solutions,":[12],"that,":[13],"for":[14,26],"subcritical":[16],"phase":[17],"and":[18],"$0<\u03b1\\le1$,":[20],"oscillation-based":[21],"interior":[22,40],"$C^\u03b1$":[23],"estimates":[24],"fail":[25],"the":[27],"special":[28],"Lagrangian":[29],"equation":[30],"in":[31],"$\\mathbb{R}^n$.":[32],"In":[33],"fact,":[34],"this":[35],"has":[37],"no":[38],"common":[39],"modulus":[41],"continuity.":[43]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-03T00:00:00"}
