{"id":"https://openalex.org/W3105215419","doi":"https://doi.org/10.1007/s00028-022-00805-7","title":"Uniqueness for degenerate parabolic equations in weighted $$L^1$$ spaces","display_name":"Uniqueness for degenerate parabolic equations in weighted $$L^1$$ spaces","publication_year":2022,"publication_date":"2022-05-26","ids":{"openalex":"https://openalex.org/W3105215419","doi":"https://doi.org/10.1007/s00028-022-00805-7","mag":"3105215419"},"language":"en","primary_location":{"id":"doi:10.1007/s00028-022-00805-7","doi":"https://doi.org/10.1007/s00028-022-00805-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00028-022-00805-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00028-022-00805-7.pdf","source":{"id":"https://openalex.org/S44870929","display_name":"Journal of Evolution Equations","issn_l":"1424-3199","issn":["1424-3199","1424-3202"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Evolution Equations","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00028-022-00805-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073323409","display_name":"Camilla Nobili","orcid":"https://orcid.org/0000-0001-6976-7494","observed_orcids":["https://orcid.org/0000-0001-6976-7494"]},"institutions":[{"id":"https://openalex.org/I28290843","display_name":"University of Surrey","ror":"https://ror.org/00ks66431","country_code":"GB","type":"education","lineage":["https://openalex.org/I28290843"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Camilla Nobili","raw_affiliation_strings":["Department of Mathematics, University of Surrey, Guildford, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Surrey, Guildford, United Kingdom","institution_ids":["https://openalex.org/I28290843"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053674909","display_name":"Fabio Punzo","orcid":"https://orcid.org/0000-0001-8596-894X","observed_orcids":["https://orcid.org/0000-0001-8596-894X"]},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Fabio Punzo","raw_affiliation_strings":["Dipartimento di Matematica, Politecnico di Milano, Milan, Italia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica, Politecnico di Milano, Milan, Italia","institution_ids":["https://openalex.org/I93860229"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5053674909"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":{"value":2890,"currency":"USD","value_usd":2890},"fwci":0.8227,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.62977465,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"22","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.913100004196167,"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":0.913100004196167,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.07530000060796738,"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/T11049","display_name":"Advanced Harmonic Analysis Research","score":0.002099999925121665,"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/degenerate-parabolic-equations","display_name":"degenerate parabolic equations","score":0.9359999895095825},{"id":"https://openalex.org/keywords/uniqueness-of-solutions","display_name":"uniqueness of solutions","score":0.9909999966621399},{"id":"https://openalex.org/keywords/weighted-l1-spaces","display_name":"weighted L1 spaces","score":0.968999981880188},{"id":"https://openalex.org/keywords/unbounded-solutions","display_name":"unbounded solutions","score":0.7319999933242798},{"id":"https://openalex.org/keywords/integral-conditions","display_name":"integral conditions","score":0.6660000085830688},{"id":"https://openalex.org/keywords/bounded-domains","display_name":"bounded domains","score":0.7760000228881836},{"id":"https://openalex.org/keywords/free-boundary-conditions","display_name":"free boundary conditions","score":0.44999998807907104}],"concepts":[{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.9599639177322388},{"id":"https://openalex.org/C72319582","wikidata":"https://www.wikidata.org/wiki/Q584304","display_name":"Degenerate energy levels","level":2,"score":0.8100811839103699},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7505295276641846},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7233642339706421},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5249119997024536},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4947587847709656},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4872209131717682},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4640803337097168},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.42586076259613037},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3909655511379242},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37847816944122314},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1522682011127472},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08323252201080322},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.046924591064453125},{"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00028-022-00805-7","doi":"https://doi.org/10.1007/s00028-022-00805-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00028-022-00805-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00028-022-00805-7.pdf","source":{"id":"https://openalex.org/S44870929","display_name":"Journal of Evolution Equations","issn_l":"1424-3199","issn":["1424-3199","1424-3202"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Evolution Equations","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:2011.06867","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2011.06867","pdf_url":"https://arxiv.org/pdf/2011.06867","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":"pmh:oai:re.public.polimi.it:11311/1220627","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11311/1220627","pdf_url":"https://re.public.polimi.it/bitstream/11311/1220627/2/11311-1220627_Nobili.pdf","source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.2011.06867","doi":"https://doi.org/10.48550/arxiv.2011.06867","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2011.06867","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":"doi:10.1007/s00028-022-00805-7","doi":"https://doi.org/10.1007/s00028-022-00805-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00028-022-00805-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00028-022-00805-7.pdf","source":{"id":"https://openalex.org/S44870929","display_name":"Journal of Evolution Equations","issn_l":"1424-3199","issn":["1424-3199","1424-3202"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","dongbi-b","jufo-1","norway-1","poland-100","russia-white-list-1"],"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Evolution Equations","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3105215419.pdf","grobid_xml":"https://content.openalex.org/works/W3105215419.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W275238597","https://openalex.org/W639693100","https://openalex.org/W1525786255","https://openalex.org/W1698081298","https://openalex.org/W1797800508","https://openalex.org/W2002237777","https://openalex.org/W2027576481","https://openalex.org/W2028121921","https://openalex.org/W2048998441","https://openalex.org/W2050786338","https://openalex.org/W2054579041","https://openalex.org/W2069663188","https://openalex.org/W2089236060","https://openalex.org/W2253394628","https://openalex.org/W2294220765","https://openalex.org/W2315214156","https://openalex.org/W2325767822","https://openalex.org/W2333691629","https://openalex.org/W2340482820","https://openalex.org/W2946437452","https://openalex.org/W2954526116"],"related_works":["https://openalex.org/W2954526116","https://openalex.org/W2002237777","https://openalex.org/W7095623227","https://openalex.org/W195950189","https://openalex.org/W2529198396","https://openalex.org/W2353847557","https://openalex.org/W2736301112","https://openalex.org/W4286652362","https://openalex.org/W2072998957","https://openalex.org/W1996310820"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"study":[2],"uniqueness":[3,26],"of":[4],"solutions":[5,30,45],"to":[6,47],"degenerate":[7],"parabolic":[8],"problems,":[9],"posed":[10],"in":[11,37],"bounded":[12],"domains,":[13],"where":[14],"no":[15],"boundary":[16],"conditions":[17],"are":[18],"imposed.":[19],"Under":[20],"suitable":[21,49],"assumptions":[22],"on":[23],"the":[24],"operator,":[25],"is":[27],"obtained":[28],"for":[29,42],"that":[31],"satisfy":[32],"an":[33],"appropriate":[34],"integral":[35],"condition;":[36],"particular,":[38],"such":[39],"condition":[40],"holds":[41],"possibly":[43],"unbounded":[44],"belonging":[46],"a":[48],"weighted":[50],"$$L^1$$":[51],"L":[52],"1":[53],"space.":[54]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2020-11-23T00:00:00"}