{"id":"https://openalex.org/W2099187870","doi":"https://doi.org/10.1137/130917314","title":"Second-Order and Stability Analysis for State-Constrained Elliptic Optimal Control Problems with Sparse Controls","display_name":"Second-Order and Stability Analysis for State-Constrained Elliptic Optimal Control Problems with Sparse Controls","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2099187870","doi":"https://doi.org/10.1137/130917314","mag":"2099187870"},"language":"en","primary_location":{"id":"doi:10.1137/130917314","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130917314","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":true,"oa_status":"green","oa_url":"http://hdl.handle.net/10902/4884","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5067757319","display_name":"Eduardo Casas","orcid":"https://orcid.org/0000-0002-8364-9416"},"institutions":[{"id":"https://openalex.org/I13134134","display_name":"Universidad de Cantabria","ror":"https://ror.org/046ffzj20","country_code":"ES","type":"education","lineage":["https://openalex.org/I13134134"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Eduardo Casas","raw_affiliation_strings":["University Of Cantabria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University Of Cantabria","institution_ids":["https://openalex.org/I13134134"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082981580","display_name":"Fredi Tr\u00f6ltzsch","orcid":"https://orcid.org/0000-0002-7679-3233"},"institutions":[{"id":"https://openalex.org/I4577782","display_name":"Technische Universit\u00e4t Berlin","ror":"https://ror.org/03v4gjf40","country_code":"DE","type":"education","lineage":["https://openalex.org/I4577782"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Fredi Tr\u00f6ltzsch","raw_affiliation_strings":["Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, D-10623 Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematik, Technische Universit\u00e4t Berlin, D-10623 Berlin, Germany","institution_ids":["https://openalex.org/I4577782"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.1193,"has_fulltext":false,"cited_by_count":23,"citation_normalized_percentile":{"value":0.90836496,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"52","issue":"2","first_page":"1010","last_page":"1033"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9993000030517578,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9984999895095825,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.8888863921165466},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8491075038909912},{"id":"https://openalex.org/keywords/optimal-control","display_name":"Optimal control","score":0.7788457870483398},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5316287279129028},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5266256928443909},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4871492087841034},{"id":"https://openalex.org/keywords/elliptic-partial-differential-equation","display_name":"Elliptic partial differential equation","score":0.4752112329006195},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4428972005844116},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4276660680770874},{"id":"https://openalex.org/keywords/pointwise-convergence","display_name":"Pointwise convergence","score":0.4248808026313782},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.3978385925292969},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20438778400421143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08866927027702332},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.06705376505851746}],"concepts":[{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.8888863921165466},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8491075038909912},{"id":"https://openalex.org/C91575142","wikidata":"https://www.wikidata.org/wiki/Q1971426","display_name":"Optimal control","level":2,"score":0.7788457870483398},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5316287279129028},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5266256928443909},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4871492087841034},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.4752112329006195},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4428972005844116},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4276660680770874},{"id":"https://openalex.org/C27156116","wikidata":"https://www.wikidata.org/wiki/Q1778098","display_name":"Pointwise convergence","level":3,"score":0.4248808026313782},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.3978385925292969},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20438778400421143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08866927027702332},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.06705376505851746},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/130917314","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130917314","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:repositorio.unican.es:10902/4884","is_oa":true,"landing_page_url":"http://hdl.handle.net/10902/4884","pdf_url":null,"source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"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":"SIAM Journal on Control and Optimization, 2014, 52(2), 1010\u20131033","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:repositorio.unican.es:10902/4884","is_oa":true,"landing_page_url":"http://hdl.handle.net/10902/4884","pdf_url":null,"source":{"id":"https://openalex.org/S4306400398","display_name":"UCrea (University of Cantabria)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I13134134","host_organization_name":"Universidad de Cantabria","host_organization_lineage":["https://openalex.org/I13134134"],"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":"SIAM Journal on Control and Optimization, 2014, 52(2), 1010\u20131033","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5965960305","display_name":null,"funder_award_id":"MTM2011-22711","funder_id":"https://openalex.org/F4320321837","funder_display_name":"Ministerio de Econom\u00eda y Competitividad"}],"funders":[{"id":"https://openalex.org/F4320314997","display_name":"Strong","ror":"https://ror.org/041vyzr56"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W1551360398","https://openalex.org/W1601741115","https://openalex.org/W1820125862","https://openalex.org/W1866311589","https://openalex.org/W1963754437","https://openalex.org/W1969031634","https://openalex.org/W1973494638","https://openalex.org/W1981343212","https://openalex.org/W1983938029","https://openalex.org/W1988428054","https://openalex.org/W1996088437","https://openalex.org/W2002230262","https://openalex.org/W2002996216","https://openalex.org/W2007176686","https://openalex.org/W2015783980","https://openalex.org/W2030036911","https://openalex.org/W2043093409","https://openalex.org/W2046922593","https://openalex.org/W2085831953","https://openalex.org/W2091982747","https://openalex.org/W2095140771","https://openalex.org/W2097135693","https://openalex.org/W2105253623","https://openalex.org/W2144047659","https://openalex.org/W2167025288","https://openalex.org/W4293032004"],"related_works":["https://openalex.org/W2093422383","https://openalex.org/W2931079280","https://openalex.org/W2776640168","https://openalex.org/W2046496515","https://openalex.org/W2085510698","https://openalex.org/W2466242173","https://openalex.org/W4247762935","https://openalex.org/W1976342131","https://openalex.org/W1972598260","https://openalex.org/W2043909370"],"abstract_inverted_index":{"An":[0],"optimal":[1,52,69],"control":[2,16,20,38,53],"problem":[3],"for":[4,71,75],"a":[5],"semilinear":[6],"elliptic":[7],"partial":[8],"differential":[9],"equation":[10],"is":[11,30,82],"discussed":[12],"subject":[13],"to":[14,48,64],"pointwise":[15],"constraints":[17],"on":[18],"the":[19,22,28,31,34,37,42,51,66,76],"and":[21],"state.":[23],"The":[24,78],"main":[25],"novelty":[26],"of":[27,33,36,41,50,68],"paper":[29],"presence":[32],"$L^1$-norm":[35],"as":[39],"part":[40],"objective":[43],"functional":[44],"that":[45],"eventually":[46],"leads":[47],"sparsity":[49],"functions.":[54],"Second-order":[55],"sufficient":[56],"optimality":[57],"conditions":[58],"are":[59,62],"analyzed.":[60],"They":[61],"applied":[63],"show":[65],"convergence":[67,80],"solutions":[70],"vanishing":[72],"$L^2$-regularization":[73],"parameter":[74],"control.":[77],"associated":[79],"rate":[81],"estimated.":[83]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
