{"id":"https://openalex.org/W7214613478","doi":"https://doi.org/10.48550/arxiv.2609.31353","title":"Semilinear Neumann boundary value problems for measure-valued maps","display_name":"Semilinear Neumann boundary value problems for measure-valued maps","publication_year":2026,"publication_date":"2026-09-25","ids":{"openalex":"https://openalex.org/W7214613478","doi":"https://doi.org/10.48550/arxiv.2609.31353"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.31353","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31353","pdf_url":"https://arxiv.org/pdf/2609.31353","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/2609.31353","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5094018469","display_name":"Aleksei Kroshnin","orcid":"https://orcid.org/0000-0003-3321-6409","observed_orcids":["https://orcid.org/0000-0003-3321-6409"]},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Kroshnin, Aleksei","raw_affiliation_strings":["Weierstrass Institute , Anton-Wilhelm-Amo-Strasse 39 , 10117 Berlin , Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institute , Anton-Wilhelm-Amo-Strasse 39 , 10117 Berlin , Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011294000","display_name":"Hugo Lavenant","orcid":"https://orcid.org/0000-0002-2597-1124","observed_orcids":["https://orcid.org/0000-0002-2597-1124"]},"institutions":[{"id":"https://openalex.org/I71209653","display_name":"Bocconi University","ror":"https://ror.org/05crjpb27","country_code":"IT","type":"education","lineage":["https://openalex.org/I71209653"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Lavenant, Hugo","raw_affiliation_strings":["Department of Decision Sciences and BIDSA , Bocconi University , Via Roentgen 1 , 20136 Milano , Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Decision Sciences and BIDSA , Bocconi University , Via Roentgen 1 , 20136 Milano , Italy","institution_ids":["https://openalex.org/I71209653"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5088022283","display_name":"\u0414\u043c\u0438\u0442\u0440\u0438\u0439 \u0410\u043b\u0435\u043a\u0441\u0430\u043d\u0434\u0440\u043e\u0432\u0438\u0447 \u0412\u043e\u0440\u043e\u0442\u043d\u0438\u043a\u043e\u0432","orcid":"https://orcid.org/0000-0003-1547-2572","observed_orcids":["https://orcid.org/0000-0003-1547-2572"]},"institutions":[{"id":"https://openalex.org/I4405252691","display_name":"Centro de Matem\u00e1tica","ror":"https://ror.org/0267j0k26","country_code":"PT","type":"education","lineage":["https://openalex.org/I4405252691"]},{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Vorotnikov, Dmitry","raw_affiliation_strings":["University of Coimbra , CMUC , Department of Mathematics , 3001-501 Coimbra , Portugal"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Coimbra , CMUC , Department of Mathematics , 3001-501 Coimbra , Portugal","institution_ids":["https://openalex.org/I4405252691","https://openalex.org/I76903346"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.7085000276565552,"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":0.7085000276565552,"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":0.2750999927520752,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0031999999191612005,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/neumann-problem","display_name":"Neumann problem","score":0.7540000081062317},{"id":"https://openalex.org/keywords/nonhomogeneous-boundary-conditions","display_name":"nonhomogeneous boundary conditions","score":0.7979999780654907},{"id":"https://openalex.org/keywords/existence-of-minimizers","display_name":"existence of minimizers","score":0.9369999766349792},{"id":"https://openalex.org/keywords/optimality-conditions","display_name":"optimality conditions","score":0.9950000047683716},{"id":"https://openalex.org/keywords/pressureless-euler-equations","display_name":"pressureless Euler equations","score":0.9860000014305115},{"id":"https://openalex.org/keywords/variational-problems","display_name":"variational problems","score":0.6060000061988831}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7997999787330627},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.7414000034332275},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.5508000254631042},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.5285999774932861},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5271000266075134},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5196999907493591},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.515500009059906},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4839000105857849},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.450300008058548},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4341999888420105},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4140999913215637},{"id":"https://openalex.org/C2780580338","wikidata":"https://www.wikidata.org/wiki/Q577835","display_name":"Adjunction","level":2,"score":0.40070000290870667},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.39399999380111694},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.3560999929904938},{"id":"https://openalex.org/C2775918384","wikidata":"https://www.wikidata.org/wiki/Q4660961","display_name":"A priori estimate","level":2,"score":0.3357999920845032},{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.33169999718666077},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.32420000433921814},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.30790001153945923},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.2766000032424927},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.27390000224113464},{"id":"https://openalex.org/C80469333","wikidata":"https://www.wikidata.org/wiki/Q189088","display_name":"Von Neumann architecture","level":2,"score":0.27390000224113464},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C167879884","wikidata":"https://www.wikidata.org/wiki/Q727568","display_name":"Balanced flow","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.25040000677108765}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.31353","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31353","pdf_url":"https://arxiv.org/pdf/2609.31353","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.2609.31353","doi":"https://doi.org/10.48550/arxiv.2609.31353","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.31353","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:2609.31353","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.31353","pdf_url":"https://arxiv.org/pdf/2609.31353","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":[{"id":"https://openalex.org/F4320323392","display_name":"Universidade de Coimbra","ror":"https://ror.org/04z8k9a98"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214613478.pdf","grobid_xml":"https://content.openalex.org/works/W7214613478.grobid-xml"},"referenced_works_count":3,"referenced_works":["https://openalex.org/W4406273408","https://openalex.org/W7125826622","https://openalex.org/W7143946288"],"related_works":["https://openalex.org/W2051763648","https://openalex.org/W7098736825","https://openalex.org/W7029928274","https://openalex.org/W7043734130","https://openalex.org/W2064554513","https://openalex.org/W2524654650","https://openalex.org/W4200633479","https://openalex.org/W2938485088","https://openalex.org/W2945810556","https://openalex.org/W7165839269"],"abstract_inverted_index":{"We":[0,14,29],"study":[1],"the":[2,16,24,32,76,88,91,98,109,119],"Wasserstein":[3],"lift":[4],"of":[5,18,26,42,100,111],"nonlinear":[6,120],"Poisson":[7],"systems":[8],"with":[9],"inhomogeneous":[10],"Neumann":[11],"boundary":[12],"conditions.":[13],"establish":[15],"existence":[17],"minimizers":[19,48,64],"using":[20],"new":[21,117],"estimates":[22],"involving":[23],"$p$-moments":[25],"measure-valued":[27,63,106],"traces.":[28],"also":[30],"derive":[31],"optimality":[33],"conditions,":[34],"which":[35,75],"turn":[36],"out":[37],"to":[38,90],"be":[39],"matrix-valued":[40],"generalizations":[41],"pressureless":[43],"Euler":[44],"equations.":[45],"While":[46],"deterministic":[47],"exist":[49],"under":[50],"suitable":[51],"convexity":[52],"assumptions":[53],"and":[54,78],"for":[55],"one-dimensional":[56],"source":[57],"domains,":[58],"we":[59,71],"show":[60],"that":[61],"genuinely":[62],"arise":[65],"in":[66,74,118],"higher":[67],"dimensions.":[68],"In":[69],"particular,":[70],"construct":[72],"examples":[73],"lifted":[77,92],"classical":[79],"variational":[80],"problems":[81],"have":[82],"different":[83],"minimum":[84],"values,":[85],"thereby":[86],"precluding":[87],"solutions":[89],"problem":[93],"from":[94],"being":[95],"deterministic,":[96],"despite":[97],"absence":[99],"any":[101],"a":[102],"priori":[103],"mechanism":[104],"enforcing":[105],"behavior.":[107],"To":[108],"best":[110],"our":[112],"knowledge,":[113],"this":[114],"phenomenon":[115],"is":[116],"elliptic":[121],"theory.":[122]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-29T00:00:00"}