EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP H^n
The purpose of this paper is to prove existence of minimisers of the functional J(K, u) :=∫Ω/kf(Lu)dx+α∫Ω/k|u-g|^qdx+βSd^Q-1(K∩Ω),where Ω is an open set of the Heisenberg group H^n, K runs over all closed sets of H^n, u varies in CH^1(Ω\K), α, β >0, q ≥1, g∈ L^q(Ω) ∩L^∞(Ω) and f : R^2n →R is a co...
Saved in:
| Published in | Acta mathematica scientia Vol. 25; no. 3; pp. 455 - 469 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
01.07.2005
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(05)60009-4 |
Cover
| Abstract | The purpose of this paper is to prove existence of minimisers of the functional J(K, u) :=∫Ω/kf(Lu)dx+α∫Ω/k|u-g|^qdx+βSd^Q-1(K∩Ω),where Ω is an open set of the Heisenberg group H^n, K runs over all closed sets of H^n, u varies in CH^1(Ω\K), α, β >0, q ≥1, g∈ L^q(Ω) ∩L^∞(Ω) and f : R^2n →R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below). |
|---|---|
| AbstractList | The purpose of this paper is to prove existence of minimisers of the functional J(K, u) :=∫Ω/kf(Lu)dx+α∫Ω/k|u-g|^qdx+βSd^Q-1(K∩Ω),where Ω is an open set of the Heisenberg group H^n, K runs over all closed sets of H^n, u varies in CH^1(Ω\K), α, β >0, q ≥1, g∈ L^q(Ω) ∩L^∞(Ω) and f : R^2n →R is a convex function satisfying some structure conditions (H1)(H2)(H3) (see below). |
| Author | 宋迎清 杨孝平 秦姣华 |
| AuthorAffiliation | DepartmentofMathematics＆.Calculation,HunanCityUniversity,Yiyang413000,China SchoolofScience,NanjingUniversityofScience＆Technology,Nanjing210094,China |
| Author_xml | – sequence: 1 fullname: 宋迎清 杨孝平 秦姣华 |
| BookMark | eNqFkMFOg0AQhjemJtbqI5hsPOkBnV12ocRTi0vZhEIDNNFLN1u6VLRShV58e2ltPHjxNMnMfH_yf-eoV29rg9AVgTsCxLnPgHJqeQ7QG-C3DgB4FjtBfcLdbg1Dt4f6vy9n6LxtX6HjqMP6aCGeZJaL2Bc4CfBUxnIqM5FmOEhSPMJ-NMqy_SVIhcCPMvOTOJfxXObPeJYm40hMMyxjnIcCh6Ij47FIJ3iSJvMZDhf1BTot9aY1l8c5QPNA5H5oRclE-qPIKgjlzGJ86VBqDHdNCRwKvXLAZktql6UZck08b2iA23ylXUqh5EBW7gqYy-hQd8UKe4D4T27RbNu2MaX6aKp33XwpAmovSR0kqb0BBVwdJCnWcQ9_uKLa6V21rXeNrjb_0tdH-mVbrz-req2Wungrq41RxAHPYQTsb5lAcMs |
| CitedBy_id | crossref_primary_10_1016_S0252_9602_17_30129_7 |
| Cites_doi | 10.1016/S0022-247X(03)00560-2 10.1007/BF01052971 10.1006/aima.2000.1963 10.1007/s002080100228 10.1007/s005260000076 10.1002/(SICI)1097-0312(199610)49:10<1081::AID-CPA3>3.0.CO;2-A |
| ContentType | Journal Article |
| DBID | 2RA 92L CQIGP W94 ~WA AAYXX CITATION |
| DOI | 10.1016/S0252-9602(05)60009-4 |
| DatabaseName | 维普期刊资源整合服务平台 中文科技期刊数据库-CALIS站点 维普中文期刊数据库 中文科技期刊数据库-自然科学 中文科技期刊数据库- 镜像站点 CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics Physics |
| EISSN | 1572-9087 |
| EndPage | 469 |
| ExternalDocumentID | 10_1016_S0252_9602_05_60009_4 16096410 |
| GroupedDBID | --K --M -01 -0A -EM -SA -S~ .~1 0R~ 1B1 1~. 1~5 23M 2B. 2C. 2RA 4.4 406 457 4G. 5GY 5VR 5VS 5XA 5XB 5XL 7-5 71M 8P~ 92E 92I 92L 92M 92Q 93N 9D9 9DA AACTN AAEDT AAFGU AAHNG AAIKJ AAKOC AALMO AALRI AAOAW AAPBV AAQFI AAUYE AAXUO ABAOU ABECU ABFGW ABFNM ABFTV ABKAS ABKCH ABMAC ABMQK ABPIF ABTEG ABTMW ABXDB ABXPI ABYKQ ACAZW ACBMV ACBRV ACBYP ACDAQ ACGFS ACHSB ACIGE ACIPQ ACMLO ACRLP ACTTH ACVWB ACWMK ADALY ADBBV ADEZE ADKNI ADMDM ADTIX ADURQ ADYFF AEBSH AEFTE AEJRE AEKER AENEX AESTI AEVTX AFKWA AFQWF AFUIB AGDGC AGGBP AGHFR AGJBK AGMZJ AGUBO AGYEJ AIAKS AIEXJ AIGVJ AIKHN AILAN AIMYW AITGF AITUG AJBFU AJDOV AJOXV AJZVZ AKQUC ALMA_UNASSIGNED_HOLDINGS AMFUW AMKLP AMRAJ AMYLF ARUGR AXJTR AXYYD BGNMA BKOJK BLXMC CAJEA CAJUS CCEZO CCVFK CDYEO CHBEP CIAHI CQIGP CS3 CSCUP CW9 EBLON EBS EFJIC EJD EO9 EP2 EP3 FA0 FDB FEDTE FIRID FNLPD FNPLU FYGXN GBLVA GJIRD HVGLF HZ~ IPNFZ J1W JUIAU JZLTJ KOM KOV LLZTM M41 M4Y MHUIS MO0 N9A NQJWS NU0 O-L O9- OAUVE OZT P-8 P-9 P2P PC. Q-- Q-0 Q38 R-A REI RIG ROL RSV RT1 S.. SDC SDF SDG SDH SES SNE SOJ SPC SRMVM SSLCW SSW SSZ T5K T8Q TCJ TGP TSG U1F U1G U5A U5K UOJIU UTJUX VFIZW W94 ZMTXR ~G- ~L9 ~WA AACDK AAEDW AAJBT AASML AATNV AATTM AAXKI AAYWO AAYXX ABAKF ABBRH ABDBE ABFSG ABJNI ABTKH ABWVN ACAOD ACDTI ACOKC ACPIV ACRPL ACSTC ACVFH ACZOJ ADCNI ADMUD ADNMO ADTPH AEFQL AEIPS AEMSY AESKC AEUPX AEZWR AFBBN AFDZB AFHIU AFOHR AFPUW AFXIZ AGCQF AGQEE AGRNS AHPBZ AHWEU AIGII AIGIU AIIUN AIXLP AKBMS AKRWK AKYEP AMXSW ANKPU ATHPR AYFIA CITATION DPUIP FIGPU HG6 IKXTQ IWAJR NPVJJ PT4 SJYHP SNPRN SOHCF SSH VEKWB |
| ID | FETCH-LOGICAL-c1254-45b622ee57ef050cad6034b23ffe85a1998e0535da7220f501d7d047428a252c3 |
| ISSN | 0252-9602 |
| IngestDate | Tue Jul 01 02:27:34 EDT 2025 Thu Apr 24 23:09:48 EDT 2025 Fri Nov 25 07:23:25 EST 2022 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 3 |
| Language | English |
| License | https://www.elsevier.com/tdm/userlicense/1.0 |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c1254-45b622ee57ef050cad6034b23ffe85a1998e0535da7220f501d7d047428a252c3 |
| Notes | 42-1227/O O411.1 O152 |
| PageCount | 15 |
| ParticipantIDs | crossref_primary_10_1016_S0252_9602_05_60009_4 crossref_citationtrail_10_1016_S0252_9602_05_60009_4 chongqing_backfile_16096410 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2005-07-00 |
| PublicationDateYYYYMMDD | 2005-07-01 |
| PublicationDate_xml | – month: 07 year: 2005 text: 2005-07-00 |
| PublicationDecade | 2000 |
| PublicationTitle | Acta mathematica scientia |
| PublicationTitleAlternate | Acta Mathematica Scientia |
| PublicationYear | 2005 |
| References | Monti (10.1016/S0252-9602(05)60009-4_bib4) 2000; 13 Yingqing (10.1016/S0252-9602(05)60009-4_bib14) 2003; 16 Ambrosio (10.1016/S0252-9602(05)60009-4_bib1) 2000 Franchi (10.1016/S0252-9602(05)60009-4_bib7) 2001; 321 Carriero (10.1016/S0252-9602(05)60009-4_bib3) 1990; 18 Federer (10.1016/S0252-9602(05)60009-4_bib11) 1969 Yingqing (10.1016/S0252-9602(05)60009-4_bib10) 2003; 24 Danielli (10.1016/S0252-9602(05)60009-4_bib12) 1998; 27 Ambrosio (10.1016/S0252-9602(05)60009-4_bib8) 2001; 159 Gromov (10.1016/S0252-9602(05)60009-4_bib6) 1996 Song (10.1016/S0252-9602(05)60009-4_bib13) 2003; 287 De Giorgi (10.1016/S0252-9602(05)60009-4_bib2) 1989; 108 Garofalo (10.1016/S0252-9602(05)60009-4_bib5) 1996; 49 Yingqing (10.1016/S0252-9602(05)60009-4_bib9) 2003; 23B |
| References_xml | – volume: 18 start-page: 321 issue: 4 year: 1990 ident: 10.1016/S0252-9602(05)60009-4_bib3 article-title: Sk-valued maps minimizing the Lp-norm of the gradient with free discontinuities publication-title: Ann Scola Norm Sup Pisa Cl Sci – volume: 24 issue: 4 year: 2003 ident: 10.1016/S0252-9602(05)60009-4_bib10 article-title: BV Functions in the Heisenberg group Hn publication-title: Chinese J Contemp Math – volume: 287 start-page: 296 year: 2003 ident: 10.1016/S0252-9602(05)60009-4_bib13 article-title: The Chain Rule of BV functions in the Heisenberg group Hn publication-title: J Math Anal Appl doi: 10.1016/S0022-247X(03)00560-2 – year: 1996 ident: 10.1016/S0252-9602(05)60009-4_bib6 article-title: Carnot-Carathéodory spaces seen from within, in sub-Riemannian geometry – volume: 108 start-page: 195 year: 1989 ident: 10.1016/S0252-9602(05)60009-4_bib2 article-title: Existence theorem for a minimum problem with free discontinuity set publication-title: Arch Rat Mech Anal doi: 10.1007/BF01052971 – volume: 159 start-page: 51 year: 2001 ident: 10.1016/S0252-9602(05)60009-4_bib8 article-title: Some fine properties of sets of finite perimeter in Ahlfors regular metric measure spaces publication-title: Adv Math doi: 10.1006/aima.2000.1963 – volume: 321 start-page: 479 year: 2001 ident: 10.1016/S0252-9602(05)60009-4_bib7 article-title: Rectifiablity and perimeter in the Hensenberg group publication-title: Math Ann doi: 10.1007/s002080100228 – year: 1969 ident: 10.1016/S0252-9602(05)60009-4_bib11 – volume: 13 start-page: 339 year: 2000 ident: 10.1016/S0252-9602(05)60009-4_bib4 article-title: Surface measures in Carnot-Carathéodory spaces publication-title: Calc doi: 10.1007/s005260000076 – volume: 49 start-page: 1081 year: 1996 ident: 10.1016/S0252-9602(05)60009-4_bib5 article-title: Isoperimetric and Sobolev inequalities for Carnot -Carathéodory spaces and the existence of minimal surfaces publication-title: Comm Pure Appl Math doi: 10.1002/(SICI)1097-0312(199610)49:10<1081::AID-CPA3>3.0.CO;2-A – volume: 16 start-page: 148 year: 2003 ident: 10.1016/S0252-9602(05)60009-4_bib14 article-title: The compactness theorem of SBVH(Ω) in the Heisenberg group Hn publication-title: J Partial Diff Eqs – volume: 23B start-page: 433 issue: 4 year: 2003 ident: 10.1016/S0252-9602(05)60009-4_bib9 article-title: Decomposition of BV functions in the Carnot-Carathéodory spaces publication-title: Acta Mathematica scientia – year: 2000 ident: 10.1016/S0252-9602(05)60009-4_bib1 – volume: 27 start-page: 195 issue: 4 year: 1998 ident: 10.1016/S0252-9602(05)60009-4_bib12 article-title: Trace inequalities for Carnot-Carathéodory spaces and applications publication-title: Ann Scuola Norm Sup Pisa CI Sci |
| SSID | ssj0016264 |
| Score | 1.6199665 |
| Snippet | The purpose of this paper is to prove existence of minimisers of the functional J(K, u) :=∫Ω/kf(Lu)dx+α∫Ω/k|u-g|^qdx+βSd^Q-1(K∩Ω),where Ω is an open set of the... |
| SourceID | crossref chongqing |
| SourceType | Enrichment Source Index Database Publisher |
| StartPage | 455 |
| SubjectTerms | 存在性 数学物理 海森伯格群 能量导数 自由连续 |
| Title | EXISTENCE OF MINIMISERS FOR A CLASS OF FREE DISCONTINUITY PROBLEMS IN THE HEISENBERG GROUP H^n |
| URI | http://lib.cqvip.com/qk/86464X/20053/16096410.html |
| Volume | 25 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV3db9MwELfQJiR44GOAKAPkByyBqg43seP0MVldNWxNpX6I8bIocRJAQAasvPDXc3ZcpxNoAqQqutq1Xfl-Pt85d2eEXvgBL8CwyMEsAUuHcV_pNRcMSlqHo9BTRWGSuM7SYLpmb874Wec6ZKJLNsWR-vnHuJL_4SqUAV91lOw_cNZ1CgVAA3_hCRyG51_xWJ4ly5U5I5pP-rMkBUG01CEDYNnpcPPTaGluJp8spOyPk-XxPF0l6TpZvYOJn8encqbjh43Tz1RCyzSWC-uI358SLptdzTVSm7z_xSV5zW0o5Ucn1onkJJIkjIkMSTwhoSQyIHFIQt7X1GhMotD8aKxpIOIRiX2oEySCT2DqgPA1EY6hgytHEty5r24ll8e9AZhGrZitrGQVUEbt7mpFbxvzbCHm78hR1ubutVsya29z-U3atwcPSzcc6OSUEw9Ic3det8U5x8NhACYb0yF5-54Q-r3-fnSyeHviXjyBfWcyjm277IK-XnfjvKT8lR1Dp-T4cNG8_waKxo5qs6OjrO6hO9a4wFGLlPvoRtUcoLvW0MBWjF8eoNszx0f4dtN4AavLB-jcAQrPJ7gDFAZA4QgbQOkaDSh8BVB4CyicpBgAhTtAYQMoPD1vHqL1RK6OpwN7AcdAgd7LYOnCSvWqiouqppyqvAyozwrPr-sq5LkOz9Q3i_AyF55Ha06HpSgpE2DS5jBXyn-E9pqLpnqMsAqEqMvcZ1WhtD4EHdcFG6qa5pUQQdFDh24eQYFTn3RasmzLrh5i25nNlM1dr69Q-Zx1ToowYKaZk1GeGeZkrIeOXLOvbfKW6xs8ufZfHKJbHdqfor3N9x_VM1BJN8VzC6NfYHVoVg |
| linkProvider | Library Specific Holdings |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=EXISTENCE+OF+MINIMISERS+FOR+A+CLASS+OF+FREE+DISCONTINUITY+PROBLEMS+IN+THE+HEISENBERG+GROUP+H%5En&rft.jtitle=Acta+mathematica+scientia&rft.au=%E5%AE%8B%E8%BF%8E%E6%B8%85+%E6%9D%A8%E5%AD%9D%E5%B9%B3+%E7%A7%A6%E5%A7%A3%E5%8D%8E&rft.date=2005-07-01&rft.issn=0252-9602&rft.eissn=1572-9087&rft.volume=25&rft.issue=3&rft.spage=455&rft.epage=469&rft_id=info:doi/10.1016%2FS0252-9602%2805%2960009-4&rft.externalDocID=16096410 |
| thumbnail_s | http://utb.summon.serialssolutions.com/2.0.0/image/custom?url=http%3A%2F%2Fimage.cqvip.com%2Fvip1000%2Fqk%2F86464X%2F86464X.jpg |