{"id":"https://openalex.org/W7214322140","doi":"https://doi.org/10.48550/arxiv.2609.29393","title":"Serrin-type overdetermined problem for the $p$-Laplacian with Robin boundary conditions","display_name":"Serrin-type overdetermined problem for the $p$-Laplacian with Robin boundary conditions","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214322140","doi":"https://doi.org/10.48550/arxiv.2609.29393"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.29393","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29393","pdf_url":"https://arxiv.org/pdf/2609.29393","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/2609.29393","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5077396138","display_name":"Luca Barbato","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Barbato, Luca","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5059033458","display_name":"Riccardo Molinarolo","orcid":"https://orcid.org/0009-0009-9960-1124","observed_orcids":["https://orcid.org/0009-0009-9960-1124"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Molinarolo, Riccardo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9731000065803528,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9731000065803528,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.02019999921321869,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.00039999998989515007,"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/p-laplacian","display_name":"p-Laplacian","score":0.9940000176429749},{"id":"https://openalex.org/keywords/robin-boundary-conditions","display_name":"Robin boundary conditions","score":0.9789999723434448},{"id":"https://openalex.org/keywords/symmetry-of-solutions","display_name":"symmetry of solutions","score":0.7929999828338623},{"id":"https://openalex.org/keywords/shape-derivative","display_name":"shape derivative","score":0.8820000290870667},{"id":"https://openalex.org/keywords/principal-curvatures","display_name":"principal curvatures","score":0.8769999742507935},{"id":"https://openalex.org/keywords/integral-identities","display_name":"integral identities","score":0.8090000152587891},{"id":"https://openalex.org/keywords/p-function","display_name":"P-function","score":0.7360000014305115},{"id":"https://openalex.org/keywords/rigidity-results","display_name":"rigidity results","score":0.8209999799728394},{"id":"https://openalex.org/keywords/alexandrov-s-theorem","display_name":"Alexandrov's theorem","score":0.7419999837875366},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.4620000123977661}],"concepts":[{"id":"https://openalex.org/C81901731","wikidata":"https://www.wikidata.org/wiki/Q331348","display_name":"Overdetermined system","level":2,"score":0.9182999730110168},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8212000131607056},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.6328999996185303},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5907999873161316},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5570999979972839},{"id":"https://openalex.org/C108257041","wikidata":"https://www.wikidata.org/wiki/Q748993","display_name":"Robin boundary condition","level":4,"score":0.5212000012397766},{"id":"https://openalex.org/C160343418","wikidata":"https://www.wikidata.org/wiki/Q185256","display_name":"Rigidity (electromagnetism)","level":2,"score":0.4828999936580658},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4431999921798706},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.382099986076355},{"id":"https://openalex.org/C42357961","wikidata":"https://www.wikidata.org/wiki/Q213363","display_name":"Open set","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.2743000090122223},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.267300009727478},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.2671999931335449},{"id":"https://openalex.org/C84545080","wikidata":"https://www.wikidata.org/wiki/Q1147936","display_name":"Condition number","level":3,"score":0.2639000117778778},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.26339998841285706},{"id":"https://openalex.org/C16977076","wikidata":"https://www.wikidata.org/wiki/Q1589551","display_name":"Principal curvature","level":4,"score":0.26030001044273376},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.258899986743927},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.2500999867916107}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.29393","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29393","pdf_url":"https://arxiv.org/pdf/2609.29393","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.2609.29393","doi":"https://doi.org/10.48550/arxiv.2609.29393","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.29393","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.29393","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.29393","pdf_url":"https://arxiv.org/pdf/2609.29393","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/G2875028031","display_name":null,"funder_award_id":"CUP B33C25000380001","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214322140.pdf","grobid_xml":"https://content.openalex.org/works/W7214322140.grobid-xml"},"referenced_works_count":2,"referenced_works":["https://openalex.org/W7164532456","https://openalex.org/W7167796881"],"related_works":["https://openalex.org/W7131288907","https://openalex.org/W7221331039","https://openalex.org/W4408783543","https://openalex.org/W7070366854","https://openalex.org/W2980994397","https://openalex.org/W4386294784","https://openalex.org/W4390110813","https://openalex.org/W7223088762","https://openalex.org/W2963044409","https://openalex.org/W7221776159"],"abstract_inverted_index":{"Let":[0,19],"$\u03a9$":[1],"be":[2],"an":[3,54],"open":[4],"bounded":[5],"connected":[6],"subset":[7],"of":[8,13,29,32,63,67,82,101],"$\\mathbb{R}^N$,":[9],"$N":[10],"\\geq":[11,21],"2$,":[12],"class":[14],"$C^{2,\u03b1}$,":[15],"for":[16],"$\u03b1\\in":[17],"(0,1)$.":[18],"$p":[20],"2$":[22],"and":[23,52,59,103],"$\u03b2>0$.":[24],"We":[25],"prove":[26,93],"the":[27,30,33,42,61,64,79,83,87,99],"symmetry":[28],"solution":[31],"$p$-torsion":[34],"problem":[35],"with":[36],"Robin":[37],"boundary":[38],"condition":[39,45,56],"subject":[40],"to":[41,53,86],"natural":[43],"overdetermined":[44],"coming":[46],"from":[47],"a":[48],"shape":[49],"derivative":[50],"argument":[51],"extra":[55],"on":[57,60,73],"$\u03b2$":[58],"minimum":[62],"principal":[65],"curvatures":[66],"$\\partial\u03a9$.":[68],"The":[69],"proof":[70],"is":[71],"based":[72],"some":[74,94],"new":[75],"integral":[76],"identities,":[77],"involving":[78],"linearized":[80],"operator":[81],"$p$-Laplacian":[84],"applied":[85],"standard":[88],"$P$-function.":[89],"In":[90],"passing":[91],"we":[92],"other":[95],"rigidity":[96],"results":[97],"in":[98],"spirit":[100],"Serrin's":[102],"Alexandrov's":[104],"Theorems.":[105]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-26T00:00:00"}