{"id":"https://openalex.org/W7203468203","doi":"https://doi.org/10.48550/arxiv.2608.12890","title":"A fractional critical problem in the halfspace with Neumann conditions","display_name":"A fractional critical problem in the halfspace with Neumann conditions","publication_year":2026,"publication_date":"2026-08-13","ids":{"openalex":"https://openalex.org/W7203468203","doi":"https://doi.org/10.48550/arxiv.2608.12890"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.12890","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.12890","pdf_url":"https://arxiv.org/pdf/2608.12890","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","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/2608.12890","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015041490","display_name":"Azahara DelaTorre","orcid":"https://orcid.org/0000-0003-1579-5187","observed_orcids":["https://orcid.org/0000-0003-1579-5187"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"DelaTorre, Azahara","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051228281","display_name":"Serena Dipierro","orcid":"https://orcid.org/0000-0003-4386-4485","observed_orcids":["https://orcid.org/0000-0003-4386-4485","https://orcid.org/0000-0001-6222-2272"]},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Dipierro, Serena","raw_affiliation_strings":["Dipartimento di Scienze di Base e Applicate per l'Ingegneria , Sapienza Universit\u00e0 di Roma , Via Antonio Scarpa 16 , 00161 Roma , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze di Base e Applicate per l'Ingegneria , Sapienza Universit\u00e0 di Roma , Via Antonio Scarpa 16 , 00161 Roma , Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051030991","display_name":"Angela Pistoia","orcid":"https://orcid.org/0000-0002-3108-8493","observed_orcids":["https://orcid.org/0000-0002-3108-8493"]},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Pistoia, Angela","raw_affiliation_strings":["Dipartimento di Scienze di Base e Applicate per l'Ingegneria , Sapienza Universit\u00e0 di Roma , Via Antonio Scarpa 16 , 00161 Roma , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze di Base e Applicate per l'Ingegneria , Sapienza Universit\u00e0 di Roma , Via Antonio Scarpa 16 , 00161 Roma , Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078447699","display_name":"Enrico Valdinoci","orcid":"https://orcid.org/0000-0001-6222-2272","observed_orcids":["https://orcid.org/0000-0001-6222-2272"]},"institutions":[{"id":"https://openalex.org/I177877127","display_name":"The University of Western Australia","ror":"https://ror.org/047272k79","country_code":"AU","type":"education","lineage":["https://openalex.org/I177877127"]},{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["AU","IT"],"is_corresponding":false,"raw_author_name":"Valdinoci, Enrico","raw_affiliation_strings":["Department of Mathematics and Statistics , The University of Western Australia , 35 Stirling Highway , Crawley WA 6009 , Australia","Dipartimento di Scienze di Base e Applicate per l'Ingegneria , Sapienza Universit\u00e0 di Roma , Via Antonio Scarpa 16 , 00161 Roma , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics , The University of Western Australia , 35 Stirling Highway , Crawley WA 6009 , Australia","institution_ids":["https://openalex.org/I177877127"]},{"raw_affiliation_string":"Dipartimento di Scienze di Base e Applicate per l'Ingegneria , Sapienza Universit\u00e0 di Roma , Via Antonio Scarpa 16 , 00161 Roma , Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"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":0.9990000128746033,"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":0.9990000128746033,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":9.999999747378752e-05,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":9.999999747378752e-05,"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/fractional-laplacian","display_name":"fractional Laplacian","score":0.968999981880188},{"id":"https://openalex.org/keywords/critical-sobolev-exponent","display_name":"critical Sobolev exponent","score":0.9200000166893005},{"id":"https://openalex.org/keywords/nontrivial-solutions","display_name":"nontrivial solutions","score":0.8489999771118164},{"id":"https://openalex.org/keywords/half-space","display_name":"half-space","score":0.46700000762939453},{"id":"https://openalex.org/keywords/nonlocal-boundary-conditions","display_name":"nonlocal boundary conditions","score":0.5550000071525574},{"id":"https://openalex.org/keywords/existence-of-solutions","display_name":"existence of solutions","score":0.621999979019165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5914999842643738},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.4968000054359436},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4860999882221222},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4047999978065491},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.36880001425743103},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3634999990463257},{"id":"https://openalex.org/C137343772","wikidata":"https://www.wikidata.org/wiki/Q584910","display_name":"Neumann series","level":2,"score":0.3544999957084656},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.3174000084400177},{"id":"https://openalex.org/C106214006","wikidata":"https://www.wikidata.org/wiki/Q1455898","display_name":"Well-posed problem","level":2,"score":0.3084000051021576},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.30720001459121704},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2858999967575073},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.27219998836517334}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.12890","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.12890","pdf_url":"https://arxiv.org/pdf/2608.12890","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2608.12890","doi":"https://doi.org/10.48550/arxiv.2608.12890","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.12890","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2608.12890","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.12890","pdf_url":"https://arxiv.org/pdf/2608.12890","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","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/W7203468203.pdf","grobid_xml":"https://content.openalex.org/works/W7203468203.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2905279937","https://openalex.org/W2997051869","https://openalex.org/W7084626436","https://openalex.org/W4400430701","https://openalex.org/W2605473193","https://openalex.org/W2243568435","https://openalex.org/W7015406651","https://openalex.org/W4387523474","https://openalex.org/W4393681150","https://openalex.org/W2803132708"],"abstract_inverted_index":{"Given":[0],"$s\\in(0,1)$":[1],"and":[2],"$n>2s$,":[3],"we":[4],"construct":[5],"nontrivial":[6],"solutions":[7],"of":[8,29],"the":[9,25],"problem":[10],"\\begin{equation*}":[11],"\\begin{cases}":[12],"(-\u0394)^s":[13],"u=u^{2^*_s-1}":[14],"&{\\mbox{":[15],"in":[16,20],"}}\\mathbb{R}^n_+,\\\\":[17],"{\\mathcal{N}}_s":[18],"u=0&{\\mbox{":[19],"}}\\mathbb{R}^n_-,\\end{cases}":[21],"\\end{equation*}where":[22],"${\\mathcal{N}}_s$":[23],"represents":[24],"nonlocal":[26],"Neumann":[27],"condition":[28],"exterior":[30],"type.":[31]},"counts_by_year":[],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-08-15T00:00:00"}