{"id":"https://openalex.org/W7214628623","doi":"https://doi.org/10.48550/arxiv.2609.30411","title":"Nondegenerate gradient Young measures and dimension reduction for nonlinear membranes","display_name":"Nondegenerate gradient Young measures and dimension reduction for nonlinear membranes","publication_year":2026,"publication_date":"2026-09-24","ids":{"openalex":"https://openalex.org/W7214628623","doi":"https://doi.org/10.48550/arxiv.2609.30411"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.30411","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30411","pdf_url":"https://arxiv.org/pdf/2609.30411","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/2609.30411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5104034836","display_name":"Gokul G. Nair","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nair, Gokul G.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027239975","display_name":"David Padilla\u2010Garza","orcid":"https://orcid.org/0000-0003-2877-8546","observed_orcids":["https://orcid.org/0000-0003-2877-8546"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Padilla-Garza, David","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5015168552","display_name":"Marco Picchi Scardaoni","orcid":"https://orcid.org/0000-0003-1348-676X","observed_orcids":["https://orcid.org/0000-0003-1348-676X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scardaoni, Marco Picchi","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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.2667999863624573,"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":0.2667999863624573,"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/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.10140000283718109,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.08479999750852585,"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/dimensionality-reduction","display_name":"dimensionality reduction","score":0.7649999856948853},{"id":"https://openalex.org/keywords/gamma-convergence","display_name":"Gamma-convergence","score":0.8059999942779541},{"id":"https://openalex.org/keywords/nonlinear-elasticity","display_name":"nonlinear elasticity","score":0.6010000109672546},{"id":"https://openalex.org/keywords/microstructure","display_name":"microstructure","score":0.6990000009536743},{"id":"https://openalex.org/keywords/relaxed-energy","display_name":"relaxed energy","score":0.550000011920929},{"id":"https://openalex.org/keywords/barycenter","display_name":"barycenter","score":0.5740000009536743}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6261000037193298},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.5990999937057495},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.564300000667572},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.5526999831199646},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5213000178337097},{"id":"https://openalex.org/C41625074","wikidata":"https://www.wikidata.org/wiki/Q176088","display_name":"Membrane","level":2,"score":0.4943999946117401},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4652999937534332},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.4332999885082245},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4180000126361847},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.40560001134872437},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.3862000107765198},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.37369999289512634},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.36959999799728394},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3531999886035919},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.33709999918937683},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32850000262260437},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C2780091087","wikidata":"https://www.wikidata.org/wiki/Q3092131","display_name":"Dimensional reduction","level":2,"score":0.3158999979496002},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.29580000042915344},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.2865999937057495},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.2847999930381775},{"id":"https://openalex.org/C2780719617","wikidata":"https://www.wikidata.org/wiki/Q1030752","display_name":"Salient","level":2,"score":0.2745000123977661},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.25220000743865967}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.30411","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30411","pdf_url":"https://arxiv.org/pdf/2609.30411","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.2609.30411","doi":"https://doi.org/10.48550/arxiv.2609.30411","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.30411","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:2609.30411","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.30411","pdf_url":"https://arxiv.org/pdf/2609.30411","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/G2018390231","display_name":null,"funder_award_id":"PRIN2022","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G231133531","display_name":null,"funder_award_id":"PRIN2022","funder_id":"https://openalex.org/F7311471023","funder_display_name":"NextGenerationEU"},{"id":"https://openalex.org/G4186925848","display_name":null,"funder_award_id":"PRIN2022","funder_id":"https://openalex.org/F4320324499","funder_display_name":"Universit\u00e0 di Pisa"},{"id":"https://openalex.org/G7263412486","display_name":"Modeling, Analysis, and Computation in Nonlinear Elasticity","funder_award_id":"2006586","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G972786147","display_name":null,"funder_award_id":"PRIN-2022","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"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"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320324499","display_name":"Universit\u00e0 di Pisa","ror":"https://ror.org/03ad39j10"},{"id":"https://openalex.org/F4320334080","display_name":"Gruppo Nazionale per la Fisica Matematica","ror":"https://ror.org/01d6bq278"},{"id":"https://openalex.org/F7311471023","display_name":"NextGenerationEU","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214628623.pdf","grobid_xml":"https://content.openalex.org/works/W7214628623.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2167308721","https://openalex.org/W7487237","https://openalex.org/W85453183","https://openalex.org/W7217502055","https://openalex.org/W3129723079","https://openalex.org/W4394639676","https://openalex.org/W2129880151","https://openalex.org/W2079440723","https://openalex.org/W2027372989","https://openalex.org/W4296775934"],"abstract_inverted_index":{"We":[0,34,98],"consider":[1],"the":[2,19,36,78,86,91,102,115],"rigorous":[3],"derivation":[4],"of":[5,15,21,43,55,76,82,107,117],"membrane":[6,49,72,88,105],"theories":[7],"from":[8],"three-dimensional":[9],"nonlinear":[10],"elasticity.":[11],"A":[12],"salient":[13],"feature":[14],"our":[16,118],"framework":[17],"is":[18,112],"inclusion":[20],"an":[22],"orientation-preservation":[23],"constraint":[24],"together":[25],"with":[26,123],"energy":[27,73,93,106],"growth":[28,94],"that":[29,101],"penalizes":[30],"vanishing":[31],"local":[32],"volume.":[33],"embed":[35],"3D":[37],"variational":[38],"problem":[39],"into":[40],"a":[41,48,53,63,70,124],"space":[42],"parametrized":[44],"measures,":[45],"and":[46,110],"obtain":[47],"$\u0393$-limit":[50],"defined":[51],"on":[52],"class":[54],"nondegenerate":[56],"gradient":[57],"Young":[58],"measures.":[59],"This":[60],"formulation":[61],"offers":[62],"twofold":[64],"advantage:":[65],"first,":[66],"it":[67],"uniquely":[68],"identifies":[69],"non-relaxed":[71],"density":[74,89],"capable":[75],"capturing":[77],"fine":[79],"oscillations":[80],"(microstructure)":[81],"minimizing":[83],"sequences;":[84],"second,":[85],"resulting":[87],"preserves":[90],"unbounded":[92],"near":[95],"degenerate":[96],"configurations.":[97],"further":[99],"show":[100],"classical":[103],"relaxed":[104],"Le":[108],"Dret":[109],"Raoult":[111],"recovered":[113],"as":[114],"minimum":[116],"functional":[119],"over":[120],"all":[121],"measures":[122,134],"prescribed":[125],"barycenter.":[126],"The":[127],"main":[128],"difficulty":[129],"lies":[130],"in":[131],"generating":[132],"such":[133],"by":[135],"maps":[136],"whose":[137],"gradients":[138],"have":[139],"rank":[140],"two":[141],"almost":[142],"everywhere,":[143],"which":[144],"we":[145],"address":[146],"through":[147],"piecewise":[148],"isometric":[149],"(origami-like)":[150],"constructions.":[151]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-29T00:00:00"}