{"id":"https://openalex.org/W7212269608","doi":"https://doi.org/10.48550/arxiv.2609.11909","title":"Global $W^{2,p}$ and $C^{2,\u03b1}$ regularity for the sigma-$2$ equation","display_name":"Global $W^{2,p}$ and $C^{2,\u03b1}$ regularity for the sigma-$2$ equation","publication_year":2026,"publication_date":"2026-09-10","ids":{"openalex":"https://openalex.org/W7212269608","doi":"https://doi.org/10.48550/arxiv.2609.11909"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.11909","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11909","pdf_url":"https://arxiv.org/pdf/2609.11909","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/2609.11909","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127330986","display_name":"Yasheng Lyu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I87445476","display_name":"Xi'an Jiaotong University","ror":"https://ror.org/017zhmm22","country_code":"CN","type":"education","lineage":["https://openalex.org/I87445476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Lyu, Yasheng","raw_affiliation_strings":["School of Mathematics and Statistics , Xi'an Jiaotong University , Xi'an , Shaanxi 710049 , People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics , Xi'an Jiaotong University , Xi'an , Shaanxi 710049 , People's Republic of China","institution_ids":["https://openalex.org/I87445476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5127330986"],"corresponding_institution_ids":["https://openalex.org/I87445476"],"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":0.5185999870300293,"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":0.5185999870300293,"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":0.46459999680519104,"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/T13080","display_name":"Advanced Differential Geometry Research","score":0.00139999995008111,"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/global-regularity","display_name":"global regularity","score":0.796999990940094},{"id":"https://openalex.org/keywords/c-2-alpha-regularity","display_name":"C^{2,alpha} regularity","score":0.9950000047683716},{"id":"https://openalex.org/keywords/prescribed-mean-curvature-equation","display_name":"prescribed mean curvature","score":0.47099998593330383}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6923999786376953},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.635200023651123},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5062000155448914},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5038999915122986},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.3646000027656555},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3571999967098236},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.3124000132083893},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2872999906539917},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.287200003862381},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.27489998936653137},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.26249998807907104}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.11909","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11909","pdf_url":"https://arxiv.org/pdf/2609.11909","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.2609.11909","doi":"https://doi.org/10.48550/arxiv.2609.11909","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.11909","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:2609.11909","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.11909","pdf_url":"https://arxiv.org/pdf/2609.11909","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/W7212269608.pdf","grobid_xml":"https://content.openalex.org/works/W7212269608.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W4415024491","https://openalex.org/W7163036931","https://openalex.org/W7204175919","https://openalex.org/W7204266197","https://openalex.org/W7204910454","https://openalex.org/W7212071055"],"related_works":["https://openalex.org/W7212071055","https://openalex.org/W3126868064","https://openalex.org/W1996704115","https://openalex.org/W7163036931","https://openalex.org/W7204266197","https://openalex.org/W1758206720","https://openalex.org/W4400435002","https://openalex.org/W2950704652","https://openalex.org/W7163597609","https://openalex.org/W3035531791"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"prove":[4],"that":[5],"continuous":[6,15],"$2$-convex":[7],"solutions":[8],"of":[9],"the":[10],"$\u03c3_{2}$":[11],"equation":[12],"with":[13,23],"positive":[14],"density":[16],"on":[17],"bounded":[18],"strictly":[19],"mean-convex":[20],"$C^{3}$":[21,24],"domains":[22],"boundary":[25],"values":[26],"belong":[27],"to":[28],"$W^{2,p}$":[29],"for":[30],"every":[31],"$1":[32]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-12T00:00:00"}