{"id":"https://openalex.org/W4285094845","doi":"https://doi.org/10.3390/sym14071423","title":"On the Existence of Radial Solutions to a Nonconstant Gradient-Constrained Problem","display_name":"On the Existence of Radial Solutions to a Nonconstant Gradient-Constrained Problem","publication_year":2022,"publication_date":"2022-07-11","ids":{"openalex":"https://openalex.org/W4285094845","doi":"https://doi.org/10.3390/sym14071423"},"language":"en","primary_location":{"id":"doi:10.3390/sym14071423","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071423","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1423/pdf?version=1657530965","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/7/1423/pdf?version=1657530965","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5021747750","display_name":"Sofia Giuffr\u00e9","orcid":"https://orcid.org/0000-0001-8503-9630"},"institutions":[{"id":"https://openalex.org/I59725666","display_name":"University of Reggio Calabria","ror":"https://ror.org/041sz8d87","country_code":"IT","type":"education","lineage":["https://openalex.org/I59725666"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Sofia Giuffr\u00e8","raw_affiliation_strings":["D.I.I.E.S, Mediterranea University of Reggio Calabria, Loc. Feo di Vito, 89122 Reggio Calabria, Italy"],"raw_orcid":"https://orcid.org/0000-0001-8503-9630","affiliations":[{"raw_affiliation_string":"D.I.I.E.S, Mediterranea University of Reggio Calabria, Loc. Feo di Vito, 89122 Reggio Calabria, Italy","institution_ids":["https://openalex.org/I59725666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089108050","display_name":"Attilio Marcian\u00f2","orcid":"https://orcid.org/0000-0002-7229-5464"},"institutions":[{"id":"https://openalex.org/I59725666","display_name":"University of Reggio Calabria","ror":"https://ror.org/041sz8d87","country_code":"IT","type":"education","lineage":["https://openalex.org/I59725666"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Attilio Marcian\u00f2","raw_affiliation_strings":["D.I.I.E.S, Mediterranea University of Reggio Calabria, Loc. Feo di Vito, 89122 Reggio Calabria, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7229-5464","affiliations":[{"raw_affiliation_string":"D.I.I.E.S, Mediterranea University of Reggio Calabria, Loc. Feo di Vito, 89122 Reggio Calabria, Italy","institution_ids":["https://openalex.org/I59725666"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5021747750"],"corresponding_institution_ids":["https://openalex.org/I59725666"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1041294,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"7","first_page":"1423","last_page":"1423"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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":0.9970999956130981,"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/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.8540152907371521},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6310309171676636},{"id":"https://openalex.org/keywords/symmetry-in-biology","display_name":"Symmetry in biology","score":0.5965316295623779},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.535892128944397},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.48058485984802246},{"id":"https://openalex.org/keywords/multiplier","display_name":"Multiplier (economics)","score":0.4532836079597473},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4380432367324829},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4316312074661255},{"id":"https://openalex.org/keywords/torsion","display_name":"Torsion (gastropod)","score":0.42905929684638977},{"id":"https://openalex.org/keywords/constraint-algorithm","display_name":"Constraint algorithm","score":0.4237048625946045},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4222245216369629},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32954955101013184},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14144599437713623},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1359443962574005}],"concepts":[{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.8540152907371521},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6310309171676636},{"id":"https://openalex.org/C64089718","wikidata":"https://www.wikidata.org/wiki/Q598159","display_name":"Symmetry in biology","level":2,"score":0.5965316295623779},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.535892128944397},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.48058485984802246},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.4532836079597473},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4380432367324829},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4316312074661255},{"id":"https://openalex.org/C77461463","wikidata":"https://www.wikidata.org/wiki/Q7827201","display_name":"Torsion (gastropod)","level":2,"score":0.42905929684638977},{"id":"https://openalex.org/C15980293","wikidata":"https://www.wikidata.org/wiki/Q5164368","display_name":"Constraint algorithm","level":3,"score":0.4237048625946045},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4222245216369629},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32954955101013184},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14144599437713623},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1359443962574005},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C139719470","wikidata":"https://www.wikidata.org/wiki/Q39680","display_name":"Macroeconomics","level":1,"score":0.0},{"id":"https://openalex.org/C141071460","wikidata":"https://www.wikidata.org/wiki/Q40821","display_name":"Surgery","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14071423","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071423","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1423/pdf?version=1657530965","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:68ca65c1769f41b68145a5553af9c45e","is_oa":true,"landing_page_url":"https://doaj.org/article/68ca65c1769f41b68145a5553af9c45e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"Symmetry, Vol 14, Iss 7, p 1423 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/7/1423/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14071423","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14071423","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14071423","pdf_url":"https://www.mdpi.com/2073-8994/14/7/1423/pdf?version=1657530965","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4285094845.pdf","grobid_xml":"https://content.openalex.org/works/W4285094845.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1913259582","https://openalex.org/W1968930982","https://openalex.org/W1984354017","https://openalex.org/W1994352610","https://openalex.org/W2052071171","https://openalex.org/W2064829290","https://openalex.org/W2068064513","https://openalex.org/W2078206210","https://openalex.org/W2120981510","https://openalex.org/W2148932990","https://openalex.org/W2226542469","https://openalex.org/W2263228084","https://openalex.org/W2612293982","https://openalex.org/W2889903677","https://openalex.org/W2999304336","https://openalex.org/W4242573138","https://openalex.org/W6693005493"],"related_works":["https://openalex.org/W2024837890","https://openalex.org/W2074745806","https://openalex.org/W1979241556","https://openalex.org/W2352028553","https://openalex.org/W1967449934","https://openalex.org/W2021667451","https://openalex.org/W4302397553","https://openalex.org/W1970808271","https://openalex.org/W2045861968","https://openalex.org/W2017306930"],"abstract_inverted_index":{"In":[0,34,105],"this":[1,53],"paper,":[2],"we":[3,64,77,97,111],"study":[4],"a":[5,72,84,113],"variational":[6],"problem":[7,42,56,90,127],"with":[8,17],"nonconstant":[9,73],"gradient":[10,18,39],"constraints.":[11],"Several":[12],"aspects":[13],"related":[14],"to":[15,125],"problems":[16],"constraints":[19],"have":[20,27],"been":[21],"studied":[22],"in":[23,31,52,91,107],"the":[24,35,41,44,58,66,79,89,92,99,108,116,121,126,129,136],"literature":[25],"and":[26,76,96,119,128],"seen":[28],"new":[29],"developments":[30],"recent":[32],"years.":[33],"case":[36],"of":[37,55,60,71,81],"constant":[38],"constraint,":[40],"is":[43,57],"well-known":[45],"elastic\u2013plastic":[46],"torsion":[47],"problem.":[48],"A":[49],"relevant":[50],"issue":[51],"type":[54],"existence":[59],"Lagrange":[61,68,131],"multipliers.":[62],"Here,":[63],"consider":[65],"equivalent":[67],"multiplier":[69],"formulation":[70],"gradient-constrained":[74],"problem,":[75],"investigate":[78],"class":[80],"solutions":[82],"having":[83],"radial":[85,93,123],"symmetry.":[86],"We":[87],"rewrite":[88],"symmetry":[94],"case,":[95,110],"analyse":[98],"different":[100],"situations":[101],"that":[102],"may":[103],"arise.":[104],"particular,":[106],"planar":[109],"derive":[112],"condition":[114],"characterizing":[115],"free":[117],"boundary":[118],"obtain":[120],"explicit":[122],"solution":[124],"Lp":[130],"multiplier.":[132],"Some":[133],"examples":[134],"support":[135],"results.":[137]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}