{"id":"https://openalex.org/W2090982358","doi":"https://doi.org/10.1137/s0363012900380425","title":"On a Constrained Dirichlet Problem","display_name":"On a Constrained Dirichlet Problem","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2090982358","doi":"https://doi.org/10.1137/s0363012900380425","mag":"2090982358"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012900380425","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900380425","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048687668","display_name":"Arrigo Cellina","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Arrigo Cellina","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5048687668"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4626,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61825243,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"41","issue":"2","first_page":"331","last_page":"344"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10545","display_name":"Optimization and Variational Analysis","score":0.9991000294685364,"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/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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9196217060089111},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.7116107940673828},{"id":"https://openalex.org/keywords/maximum-principle","display_name":"Maximum principle","score":0.7049841284751892},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.6526122689247131},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6001661419868469},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.5088256001472473},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4963894486427307},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4743815064430237},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.4694399833679199},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4627760350704193},{"id":"https://openalex.org/keywords/subderivative","display_name":"Subderivative","score":0.45048215985298157},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.44630759954452515},{"id":"https://openalex.org/keywords/euler\u2013lagrange-equation","display_name":"Euler\u2013Lagrange equation","score":0.4179898202419281},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3589639961719513},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.28026652336120605},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.21110424399375916},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.19901397824287415},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.15762841701507568},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.13799238204956055},{"id":"https://openalex.org/keywords/lagrangian","display_name":"Lagrangian","score":0.11655506491661072},{"id":"https://openalex.org/keywords/convex-optimization","display_name":"Convex optimization","score":0.09018033742904663},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07884493470191956}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9196217060089111},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7116107940673828},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.7049841284751892},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.6526122689247131},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6001661419868469},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.5088256001472473},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4963894486427307},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4743815064430237},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.4694399833679199},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4627760350704193},{"id":"https://openalex.org/C200661725","wikidata":"https://www.wikidata.org/wiki/Q289500","display_name":"Subderivative","level":4,"score":0.45048215985298157},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.44630759954452515},{"id":"https://openalex.org/C2776392105","wikidata":"https://www.wikidata.org/wiki/Q875744","display_name":"Euler\u2013Lagrange equation","level":3,"score":0.4179898202419281},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3589639961719513},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.28026652336120605},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.21110424399375916},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.19901397824287415},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.15762841701507568},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.13799238204956055},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.11655506491661072},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.09018033742904663},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07884493470191956},{"id":"https://openalex.org/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0363012900380425","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012900380425","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Control and Optimization","raw_type":"journal-article"},{"id":"pmh:oai:boa.unimib.it:10281/19686","is_oa":false,"landing_page_url":"http://hdl.handle.net/10281/19686","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2002687104","https://openalex.org/W2028144576","https://openalex.org/W2042896394","https://openalex.org/W2046074066","https://openalex.org/W2135557790","https://openalex.org/W2152867610","https://openalex.org/W2226542469"],"related_works":["https://openalex.org/W4287166808","https://openalex.org/W3172994875","https://openalex.org/W4300882938","https://openalex.org/W2804780112","https://openalex.org/W2030286963","https://openalex.org/W1966487117","https://openalex.org/W2007071827","https://openalex.org/W3120320879","https://openalex.org/W4295267471","https://openalex.org/W2518227572"],"abstract_inverted_index":{"We":[0],"consider":[1],"a":[2,7,59,73,84,91],"Dirichlet":[3],"minimum":[4,23],"problem":[5,24,43,79,85],"with":[6,25,86],"pointwise":[8],"constraint":[9],"on":[10,37],"the":[11,30,38,42,45,48,54,75,78],"gradient,":[12],"i.e.,":[13],"$\\|\\nabla":[14],"u(x)\\|":[15],"\\le":[16],"1$":[17],"a.e.,":[18],"or,":[19],"equivalently,":[20,52],"an":[21,26],"unconstrained":[22],"extended-valued":[27],"integrand.":[28],"Since":[29],"subdifferential":[31],"of":[32,44,47,53,77,83,93],"this":[33,68],"integrand":[34],"is":[35,70,88,99],"defined":[36],"whole":[39],"effective":[40],"domain,":[41],"validity":[46],"Euler--Lagrange":[49],"equation":[50,69],"(or,":[51],"Pontryagin":[55],"maximum":[56],"principle)":[57],"for":[58],"solution":[60],"w":[61],"can":[62],"be":[63],"posed.":[64],"To":[65],"show":[66],"that":[67],"verified":[71],"along":[72],"solution,":[74],"equivalence":[76],"considered":[80],"here":[81],"and":[82,90],"obstacles":[87],"proved,":[89],"generalization":[92],"Stampacchia's":[94],"bounded":[95],"slope":[96],"condition":[97],"result":[98],"presented.":[100]},"counts_by_year":[{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}