{"id":"https://openalex.org/W1532994826","doi":"https://doi.org/10.3233/asy-2012-1099","title":"Bounded solutions to the 1-Laplacian equation with a critical gradient term","display_name":"Bounded solutions to the 1-Laplacian equation with a critical gradient term","publication_year":2012,"publication_date":"2012-10-01","ids":{"openalex":"https://openalex.org/W1532994826","doi":"https://doi.org/10.3233/asy-2012-1099","mag":"1532994826"},"language":"en","primary_location":{"id":"doi:10.3233/asy-2012-1099","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2012-1099","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","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/A5037335756","display_name":"F. Andreu","orcid":null},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Fuensanta Andreu","raw_affiliation_strings":["Departament d'An\u00e0lisi Matem\u00e0tica, Universitat de Val\u00e8ncia, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament d'An\u00e0lisi Matem\u00e0tica, Universitat de Val\u00e8ncia, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034853431","display_name":"Andrea Dall\u2019Aglio","orcid":"https://orcid.org/0000-0002-4582-798X"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Andrea Dall'Aglio","raw_affiliation_strings":["Dipartimento di Matematica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, Roma, Italy. E-mail: dallaglio@mat.uniroma1.it"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Universit\u00e0 di Roma \u201cLa Sapienza\u201d, Roma, Italy. E-mail: dallaglio@mat.uniroma1.it","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5076118138","display_name":"Sergio Segura de Le\u00f3n","orcid":"https://orcid.org/0000-0002-8515-7108"},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Sergio Segura de Le\u00f3n","raw_affiliation_strings":["Departament d'An\u00e0lisi Matem\u00e0tica, Universitat de Val\u00e8ncia, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departament d'An\u00e0lisi Matem\u00e0tica, Universitat de Val\u00e8ncia, Burjassot, Valencia, Spain. E-mail: sergio.segura@uv.es","institution_ids":["https://openalex.org/I16097986"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.8182,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.6693007,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"80","issue":"1-2","first_page":"21","last_page":"43"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9998999834060669,"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.9998999834060669,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.9995999932289124,"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/bounded-function","display_name":"Bounded function","score":0.8144715428352356},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.797112226486206},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5032441020011902},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5009737014770508},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3984180986881256},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35848069190979004},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24337100982666016}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8144715428352356},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.797112226486206},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5032441020011902},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5009737014770508},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3984180986881256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35848069190979004},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24337100982666016},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3233/asy-2012-1099","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2012-1099","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma1.it:11573/498367","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/498367","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":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":18,"referenced_works":["https://openalex.org/W102577058","https://openalex.org/W1480714962","https://openalex.org/W1572548753","https://openalex.org/W1967182092","https://openalex.org/W1972008129","https://openalex.org/W1973959488","https://openalex.org/W1988716112","https://openalex.org/W2007871858","https://openalex.org/W2017231905","https://openalex.org/W2036664598","https://openalex.org/W2038353223","https://openalex.org/W2087848789","https://openalex.org/W2089231054","https://openalex.org/W2101625927","https://openalex.org/W2122833107","https://openalex.org/W2125883113","https://openalex.org/W2160310928","https://openalex.org/W2320172678"],"related_works":["https://openalex.org/W3013085049","https://openalex.org/W2319969327","https://openalex.org/W42295635","https://openalex.org/W1560496689","https://openalex.org/W4386900933","https://openalex.org/W1973996291","https://openalex.org/W4385301946","https://openalex.org/W2330575325","https://openalex.org/W4297797135","https://openalex.org/W2033441375"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3],"study":[4],"the":[5,14,30],"Dirichlet":[6],"problem":[7],"for":[8,49],"an":[9],"elliptic":[10],"equation,":[11],"in":[12,38],"which":[13],"1-Laplacian":[15],"operator":[16],"and":[17,28,55],"lower-order":[18],"terms":[19],"appear.":[20],"We":[21],"introduce":[22],"a":[23,41,46],"suitable":[24],"definition":[25],"of":[26,58],"solution":[27,37],"prove":[29],"existence":[31],"of,":[32],"at":[33],"least,":[34],"one":[35],"bounded":[36],"BV(\u03a9)":[39],"having":[40],"negligible":[42],"jump":[43],"part.":[44],"Moreover,":[45],"uniqueness":[47],"result":[48],"small":[50],"positive":[51],"data":[52],"is":[53],"proved,":[54],"explicit":[56],"examples":[57],"solutions":[59],"are":[60],"shown.":[61]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}