{"id":"https://openalex.org/W3080454149","doi":"https://doi.org/10.1137/19m1266939","title":"Sharp Regularizing Estimates for the Gain Term of the Boltzmann Collision Operator","display_name":"Sharp Regularizing Estimates for the Gain Term of the Boltzmann Collision Operator","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3080454149","doi":"https://doi.org/10.1137/19m1266939","mag":"3080454149"},"language":"en","primary_location":{"id":"doi:10.1137/19m1266939","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1266939","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical 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/A5013944242","display_name":"Jin-Cheng Jiang","orcid":"https://orcid.org/0000-0001-5726-2480"},"institutions":[{"id":"https://openalex.org/I25846049","display_name":"National Tsing Hua University","ror":"https://ror.org/00zdnkx70","country_code":"TW","type":"education","lineage":["https://openalex.org/I25846049"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Jin-Cheng Jiang","raw_affiliation_strings":["Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30013, R.O"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30013, R.O","institution_ids":["https://openalex.org/I25846049"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013944242"],"corresponding_institution_ids":["https://openalex.org/I25846049"],"apc_list":null,"apc_paid":null,"fwci":0.2915,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.50055668,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"52","issue":"4","first_page":"4068","last_page":"4100"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998000264167786,"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9995999932289124,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","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/mathematics","display_name":"Mathematics","score":0.8354699015617371},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.725059449672699},{"id":"https://openalex.org/keywords/collision","display_name":"Collision","score":0.6407361626625061},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.5828527808189392},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5774967670440674},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5719199776649475},{"id":"https://openalex.org/keywords/boltzmann-constant","display_name":"Boltzmann constant","score":0.5436441898345947},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42111936211586},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1471458375453949}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8354699015617371},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.725059449672699},{"id":"https://openalex.org/C121704057","wikidata":"https://www.wikidata.org/wiki/Q352070","display_name":"Collision","level":2,"score":0.6407361626625061},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.5828527808189392},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5774967670440674},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5719199776649475},{"id":"https://openalex.org/C35304006","wikidata":"https://www.wikidata.org/wiki/Q5962","display_name":"Boltzmann constant","level":2,"score":0.5436441898345947},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42111936211586},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1471458375453949},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1266939","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1266939","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1828302375","display_name":null,"funder_award_id":"107-2923-M-001-001","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"},{"id":"https://openalex.org/G8375963055","display_name":null,"funder_award_id":"106-2115-M-007-003","funder_id":"https://openalex.org/F4320322795","funder_display_name":"Ministry of Science and Technology, Taiwan"}],"funders":[{"id":"https://openalex.org/F4320311041","display_name":"National Center for Theoretical Sciences","ror":"https://ror.org/02mfp0b67"},{"id":"https://openalex.org/F4320322795","display_name":"Ministry of Science and Technology, Taiwan","ror":"https://ror.org/02kv4zf79"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1963966787","https://openalex.org/W1964539058","https://openalex.org/W1966202364","https://openalex.org/W1974909579","https://openalex.org/W1977907152","https://openalex.org/W1978894893","https://openalex.org/W1986392575","https://openalex.org/W1993992841","https://openalex.org/W2000316337","https://openalex.org/W2023023275","https://openalex.org/W2023869900","https://openalex.org/W2039308004","https://openalex.org/W2042069027","https://openalex.org/W2056051178","https://openalex.org/W2070117020","https://openalex.org/W2072529690","https://openalex.org/W2332204213","https://openalex.org/W2927466679","https://openalex.org/W3105803241","https://openalex.org/W4248200323"],"related_works":["https://openalex.org/W2007632118","https://openalex.org/W2076303422","https://openalex.org/W4388257265","https://openalex.org/W849161923","https://openalex.org/W4388401275","https://openalex.org/W1579959893","https://openalex.org/W3404850","https://openalex.org/W4238782814","https://openalex.org/W4386916460","https://openalex.org/W58974396"],"abstract_inverted_index":{"We":[0],"prove":[1],"the":[2,7,11,29,32,36,41,51,58,64,68,72,90,95],"sharp":[3,48],"regularizing":[4,45,92],"estimates":[5,26,79,96],"for":[6],"gain":[8,37],"term":[9,38],"of":[10,35,67,71,85,113,120],"Boltzmann":[12],"collision":[13,73],"operator,":[14],"including":[15],"hard":[16,18],"sphere,":[17],"potential,":[19],"and":[20,31,39,57],"Maxwell":[21],"molecule":[22],"models.":[23],"Our":[24],"new":[25],"characterize":[27],"both":[28,49],"regularization":[30],"convolution":[33],"properties":[34],"have":[40],"following":[42],"features.":[43],"The":[44,75],"exponent":[46,66],"is":[47,63],"in":[50,77,97,109,123],"$L^2$":[52],"based":[53],"inhomogeneous":[54],"Sobolev":[55,60,99],"spaces":[56,88,111],"homogeneous":[59,98],"spaces,":[61,100],"which":[62],"exact":[65],"kinetic":[69],"part":[70],"kernel.":[74],"functions":[76,107],"these":[78],"belong":[80],"to":[81],"a":[82],"wider":[83],"scope":[84],"(weighted)":[86],"Lebesgue":[87,110,115],"than":[89],"previous":[91],"estimates.":[93],"For":[94],"never":[101],"seen":[102],"before,":[103],"we":[104],"only":[105],"need":[106],"lying":[108],"instead":[112],"weighted":[114],"spaces;":[116],"i.e.,":[117],"no":[118],"loss":[119],"weight":[121],"occurs":[122],"this":[124],"case.":[125]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}