{"id":"https://openalex.org/W1615786081","doi":"https://doi.org/10.1137/070680825","title":"On<i>p</i>-Harmonic Map Heat Flows for $1\\leqp&lt;\\infty$ and Their Finite Element Approximations","display_name":"On<i>p</i>-Harmonic Map Heat Flows for $1\\leqp&lt;\\infty$ and Their Finite Element Approximations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1615786081","doi":"https://doi.org/10.1137/070680825","mag":"1615786081"},"language":"en","primary_location":{"id":"doi:10.1137/070680825","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070680825","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/A5071664437","display_name":"John W. Barrett","orcid":"https://orcid.org/0000-0002-4048-1692"},"institutions":[{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"John W. Barrett","raw_affiliation_strings":["Imperial College London,#TAB#"],"affiliations":[{"raw_affiliation_string":"Imperial College London,#TAB#","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011365911","display_name":"Xiaobing Feng","orcid":"https://orcid.org/0000-0002-9191-9092"},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiaobing Feng","raw_affiliation_strings":["#N##TAB##TAB##TAB##TAB# University of Tennessee#N##TAB##TAB##TAB#"],"affiliations":[{"raw_affiliation_string":"#N##TAB##TAB##TAB##TAB# University of Tennessee#N##TAB##TAB##TAB#","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046668672","display_name":"Andreas Prohl","orcid":"https://orcid.org/0000-0003-4523-9536"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Andreas Prohl","raw_affiliation_strings":["University of T\u00fcbingen"],"affiliations":[{"raw_affiliation_string":"University of T\u00fcbingen","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071664437"],"corresponding_institution_ids":["https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":1.3158,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.74197566,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"40","issue":"4","first_page":"1471","last_page":"1498"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9994000196456909,"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":0.9994000196456909,"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/T10229","display_name":"Geometric Analysis and Curvature Flows","score":0.996399998664856,"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":0.9957000017166138,"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/harmonic-map","display_name":"Harmonic map","score":0.8371690511703491},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7481819987297058},{"id":"https://openalex.org/keywords/nabla-symbol","display_name":"Nabla symbol","score":0.6514040231704712},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5567585229873657},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5486151576042175},{"id":"https://openalex.org/keywords/wedge","display_name":"Wedge (geometry)","score":0.5038782954216003},{"id":"https://openalex.org/keywords/vector-field","display_name":"Vector field","score":0.4693763256072998},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4490370452404022},{"id":"https://openalex.org/keywords/flow","display_name":"Flow (mathematics)","score":0.44832414388656616},{"id":"https://openalex.org/keywords/heat-flow","display_name":"Heat flow","score":0.43896251916885376},{"id":"https://openalex.org/keywords/weak-solution","display_name":"Weak solution","score":0.4183831214904785},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.33740562200546265},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3245566487312317},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2332037389278412},{"id":"https://openalex.org/keywords/thermal","display_name":"Thermal","score":0.17189866304397583}],"concepts":[{"id":"https://openalex.org/C6270764","wikidata":"https://www.wikidata.org/wiki/Q5659257","display_name":"Harmonic map","level":2,"score":0.8371690511703491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7481819987297058},{"id":"https://openalex.org/C54207081","wikidata":"https://www.wikidata.org/wiki/Q937750","display_name":"Nabla symbol","level":3,"score":0.6514040231704712},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5567585229873657},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5486151576042175},{"id":"https://openalex.org/C47422493","wikidata":"https://www.wikidata.org/wiki/Q2755127","display_name":"Wedge (geometry)","level":2,"score":0.5038782954216003},{"id":"https://openalex.org/C91188154","wikidata":"https://www.wikidata.org/wiki/Q186247","display_name":"Vector field","level":2,"score":0.4693763256072998},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4490370452404022},{"id":"https://openalex.org/C38349280","wikidata":"https://www.wikidata.org/wiki/Q1434290","display_name":"Flow (mathematics)","level":2,"score":0.44832414388656616},{"id":"https://openalex.org/C2985596519","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat flow","level":3,"score":0.43896251916885376},{"id":"https://openalex.org/C45137528","wikidata":"https://www.wikidata.org/wiki/Q7977966","display_name":"Weak solution","level":2,"score":0.4183831214904785},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.33740562200546265},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3245566487312317},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2332037389278412},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.17189866304397583},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"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/C2779557605","wikidata":"https://www.wikidata.org/wiki/Q9890","display_name":"Omega","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/070680825","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070680825","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"},{"id":"pmh:oai:spiral.imperial.ac.uk:10044/1/1434","is_oa":false,"landing_page_url":"http://hdl.handle.net/10044/1/1434","pdf_url":null,"source":{"id":"https://openalex.org/S4306401396","display_name":"Spiral (Imperial College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I47508984","host_organization_name":"Imperial College London","host_organization_lineage":["https://openalex.org/I47508984"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"1498","raw_type":"Journal Article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.6899999976158142,"display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W102027516","https://openalex.org/W606406026","https://openalex.org/W1480714962","https://openalex.org/W1488494310","https://openalex.org/W1524433941","https://openalex.org/W1547403762","https://openalex.org/W1553707579","https://openalex.org/W1569061876","https://openalex.org/W1582617215","https://openalex.org/W1600845614","https://openalex.org/W1650067299","https://openalex.org/W1965468781","https://openalex.org/W1974228548","https://openalex.org/W1976338362","https://openalex.org/W1982081010","https://openalex.org/W1983294388","https://openalex.org/W1984319304","https://openalex.org/W2004708748","https://openalex.org/W2010872619","https://openalex.org/W2011530793","https://openalex.org/W2019798593","https://openalex.org/W2022088322","https://openalex.org/W2027043390","https://openalex.org/W2031178551","https://openalex.org/W2034075141","https://openalex.org/W2041324809","https://openalex.org/W2041523977","https://openalex.org/W2044728570","https://openalex.org/W2045452373","https://openalex.org/W2057464224","https://openalex.org/W2063307022","https://openalex.org/W2073078790","https://openalex.org/W2081559794","https://openalex.org/W2086365560","https://openalex.org/W2087811323","https://openalex.org/W2090751519","https://openalex.org/W2092020869","https://openalex.org/W2103559027","https://openalex.org/W2120329382","https://openalex.org/W2146329425","https://openalex.org/W2313098600","https://openalex.org/W2330412353","https://openalex.org/W2369386221","https://openalex.org/W2502999678","https://openalex.org/W2605999443","https://openalex.org/W2609182578","https://openalex.org/W3149624656"],"related_works":["https://openalex.org/W3023048661","https://openalex.org/W2018970909","https://openalex.org/W2980837821","https://openalex.org/W4387225177","https://openalex.org/W2468661775","https://openalex.org/W332713575","https://openalex.org/W2025621445","https://openalex.org/W1932165975","https://openalex.org/W2092259612","https://openalex.org/W2788247819"],"abstract_inverted_index":{"Motivated":[0],"by":[1],"emerging":[2],"applications":[3],"from":[4],"imaging":[5],"processing,":[6],"this":[7],"paper":[8],"studies":[9],"the":[10,21,39,42,61,70,87,92,132,138,141],"heat":[11,73,135],"flow":[12,40],"of":[13,32,63,89,91,131,140],"a":[14,27,47,50,55,65,82,99,102,108,117],"generalized":[15],"p-harmonic":[16,133],"map":[17,72,134],"into":[18],"spheres":[19],"for":[20,38,69,127],"whole":[22],"spectrum,":[23],"$1\\leq":[24],"p<\\infty$,":[25],"in":[26],"unified":[28],"framework.":[29],"The":[30,75],"existence":[31,62],"global":[33],"weak":[34,129],"solutions":[35,130],"is":[36,58,67,84,124,145],"established":[37],"using":[41],"energy":[43],"method":[44,123,144],"together":[45],"with":[46],"regularization":[48],"and":[49,60,95,107,137],"penalization":[51],"technique.":[52],"In":[53],"particular,":[54],"$BV$-solution":[56],"concept":[57],"introduced":[59],"such":[64,81],"solution":[66],"proved":[68],"1-harmonic":[71],"flow.":[74],"main":[76],"idea":[77],"used":[78],"to":[79,85],"develop":[80],"theory":[83],"exploit":[86],"properties":[88],"measures":[90],"forms":[93],"$\\mathcal{A}\\cdot\\nabla\\mathbf{v}$":[94],"$\\mathcal{A}\\wedge\\nabla\\mathbf{v}$,":[96],"which":[97],"pair":[98],"divergence-$L^1$,":[100],"or":[101],"divergence-measure,":[103],"tensor":[104],"field":[105,110],"$\\mathcal{A}$":[106],"$BV$-vector":[109],"$\\mathbf{v}$.":[111],"Based":[112],"on":[113],"these":[114],"analytical":[115],"results,":[116],"practical":[118],"fully":[119],"discrete":[120],"finite":[121],"element":[122],"then":[125],"proposed":[126,142],"approximating":[128],"flow,":[136],"convergence":[139],"numerical":[143],"also":[146],"established.":[147]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-02T08:37:19.008085","created_date":"2025-10-10T00:00:00"}