Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types
For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an associated Lagrangian, invariance with respect to changes in independent and dependent variables is investigated, as are results in the classification of continuous one-...
Saved in:
| Published in: | Duke mathematical journal Vol. 127; no. 2; pp. 251 - 290 |
|---|---|
| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
DUKE University Press
01-04-2005
Duke University Press |
| Subjects: | |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Abstract | For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an associated Lagrangian, invariance with respect to changes in independent and dependent variables is investigated, as are results in the classification of continuous one-parameter symmetry groups. For the variational and divergence symmetries, conservation laws are derived via the method of multipliers. The conservation laws resulting from anisotropic dilations are applied to prove uniqueness theorems for linear and nonlinear problems, and the invariance under dilations of the linear part is used to derive critical exponent phenomena and to obtain localized energy estimates for supercritical problems. |
|---|---|
| AbstractList | For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an associated Lagrangian, invariance with respect to changes in independent and dependent variables is investigated, as are results in the classification of continuous one-parameter symmetry groups. For the variational and divergence symmetries, conservation laws are derived via the method of multipliers. The conservation laws resulting from anisotropic dilations are applied to prove uniqueness theorems for linear and nonlinear problems, and the invariance under dilations of the linear part is used to derive critical exponent phenomena and to obtain localized energy estimates for supercritical problems. For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an associated Lagrangian, invariance with respect to changes in independent and dependent variables is investigated, as are results in the classification of continuous one-parameter symmetry groups. For the variational and divergence symmetries, conservation laws are derived via the method of multipliers. The conservation laws resulting from anisotropic dilations are applied to prove uniqueness theorems for linear and nonlinear problems, and the invariance under dilations of the linear part is used to derive critical exponent phenomena and to obtain localized energy estimates for supercritical problems. |
| Author | Lupo, Daniela Payne, Kevin R. |
| Author_xml | – sequence: 1 givenname: Daniela surname: Lupo fullname: Lupo, Daniela – sequence: 2 givenname: Kevin R. surname: Payne fullname: Payne, Kevin R. |
| BookMark | eNo9kFtvGyEQhVGVSnUuPyESf4CG6wJvjZwmqWSpatM8IxaGFne9OLBp438f3-R5OZoz852Hc47OxjICQteMfmacqZsnShknmlpJqCSMa86J-YBmTElNtLDmDM1OL5_QeWvL3Wo7PkM_5mVsUP_5KZcRD_5_w6lUDC-ve6fhkvAqv0HEMAx5PeVA_mzWUPsy5ID9GHGE3zBC9RPgaXtpl-hj8kODq6NeoOf7r7_mj2Tx_eHb_HZBgpBmIslYk1JPFe96a4Fbbn0Kfa8VE5qHZJT0ILS0QXraM8Wjip4JwyNoKiMXF-jLIXddyxLCBK9hyNGta175unHFZzd_Xhzdo8TV0rHtdNQatYtQh4hQS2sV0olm1O2qdftq3a43R6XbV-vMliMHLrcJ3k6Qr39dp4VWTnfKMUH53c-7LSXeAacjfro |
| CitedBy_id | crossref_primary_10_1007_s00032_021_00326_x crossref_primary_10_2140_pjm_2018_296_181 crossref_primary_10_1142_S0219199711004531 crossref_primary_10_1016_j_na_2014_05_009 crossref_primary_10_2140_pjm_2021_314_29 crossref_primary_10_1007_s10231_005_0173_5 crossref_primary_10_1007_s11856_009_0097_7 crossref_primary_10_1016_j_jde_2017_08_033 crossref_primary_10_1016_j_geomphys_2008_03_003 crossref_primary_10_1088_1751_8113_44_9_095004 crossref_primary_10_1016_j_aml_2010_12_005 crossref_primary_10_1016_j_jmaa_2006_11_012 |
| Cites_doi | 10.1007/978-1-4612-4350-2 10.1002/cpa.3160360405 10.1215/S0012-7094-77-04430-1 10.1515/9781400863174 10.1098/rspa.1956.0119 10.1002/cpa.3160090104 10.1215/S0012-7094-99-09814-9 10.1512/iumj.1953.2.52005 10.1006/jdeq.2001.4139 10.2307/2946554 10.1002/cpa.3160110306 10.1002/cpa.3160140327 10.1090/cbms/073 10.1007/s10231-005-0173-5 10.1090/S0273-0979-00-00857-0 10.1002/cpa.3160450604 10.1002/cpa.3031 10.1016/B978-0-12-531680-4.50012-5 10.1002/cpa.3160390607 10.1002/cpa.3160060402 10.1512/iumj.1992.41.41005 |
| ContentType | Journal Article |
| Copyright | Copyright 2005 Duke University Press |
| Copyright_xml | – notice: Copyright 2005 Duke University Press |
| DBID | BSCLL AAYXX CITATION |
| DOI | 10.1215/S0012-7094-04-12722-8 |
| DatabaseName | Istex CrossRef |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 1547-7398 |
| EndPage | 290 |
| ExternalDocumentID | oai_CULeuclid_euclid_dmj_1111609852 10_1215_S0012_7094_04_12722_8 ark_67375_765_1302DRD4_1 |
| GroupedDBID | --Z -ET -~X 186 6TJ ABCQX ABDNZ ABZEH ACNCT ACUXE ADNWM AEILP AENEX AI. AINRN ALMA_UNASSIGNED_HOLDINGS BSCLL CS3 DU5 EBS EJD H~9 K-O L7B MVM OHT P2P PUASD RBU RDP RDU RPE S10 SJN TN5 TWZ UPT VH1 VQP WH7 XOL XSW ZCG AAYXX CITATION 08R AALRV ABEFU ABFLS ACYGS ADYLN AETEA AFMIJ ET F20 FA8 QZG X XJT Z ZKB ZY4 |
| ID | FETCH-LOGICAL-c348t-f898ffb0526b99e2929afcbb751372cf854ae3749c4a0b152d5da1382de704d23 |
| ISSN | 0012-7094 |
| IngestDate | Sat Jan 08 04:19:04 EST 2022 Thu Nov 21 22:49:40 EST 2024 Wed Oct 30 09:31:43 EDT 2024 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c348t-f898ffb0526b99e2929afcbb751372cf854ae3749c4a0b152d5da1382de704d23 |
| Notes | zbl:1078.35078 pii:S0012-7094-04-12722-8 pe:euclid.dmj/1111609852 mr:2130413 istex:657058C3DB7EB20E5A410809E75FC855A83E7620 ark:/67375/765-1302DRD4-1 doi:10.1215/S0012-7094-04-12722-8 |
| PageCount | 40 |
| ParticipantIDs | projecteuclid_primary_oai_CULeuclid_euclid_dmj_1111609852 crossref_primary_10_1215_S0012_7094_04_12722_8 istex_primary_ark_67375_765_1302DRD4_1 |
| PublicationCentury | 2000 |
| PublicationDate | 2005-04-01 |
| PublicationDateYYYYMMDD | 2005-04-01 |
| PublicationDate_xml | – month: 04 year: 2005 text: 2005-04-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationTitle | Duke mathematical journal |
| PublicationYear | 2005 |
| Publisher | DUKE University Press Duke University Press |
| Publisher_xml | – name: DUKE University Press – name: Duke University Press |
| References | 22 24 25 26 27 28 29 30 31 10 32 11 33 12 34 13 14 15 cr-split#-23.1 16 cr-split#-23.2 17 18 19 1 2 3 4 5 6 7 8 9 20 21 |
| References_xml | – ident: 24 doi: 10.1007/978-1-4612-4350-2 – ident: 4 doi: 10.1002/cpa.3160360405 – ident: 32 doi: 10.1215/S0012-7094-77-04430-1 – ident: 12 – ident: 5 doi: 10.1515/9781400863174 – ident: 19 doi: 10.1098/rspa.1956.0119 – ident: 20 doi: 10.1002/cpa.3160090104 – ident: 33 – ident: 2 doi: 10.1215/S0012-7094-99-09814-9 – ident: 28 doi: 10.1512/iumj.1953.2.52005 – ident: 14 – ident: 17 doi: 10.1006/jdeq.2001.4139 – ident: 29 doi: 10.2307/2946554 – ident: 8 doi: 10.1002/cpa.3160110306 – ident: 21 doi: 10.1002/cpa.3160140327 – ident: #cr-split#-23.1 – ident: 31 doi: 10.1090/cbms/073 – ident: 9 – ident: 26 doi: 10.1007/s10231-005-0173-5 – ident: 7 – ident: 22 doi: 10.1090/S0273-0979-00-00857-0 – ident: 3 – ident: 11 – ident: 13 doi: 10.1002/cpa.3160450604 – ident: 18 doi: 10.1002/cpa.3031 – ident: 34 – ident: 15 – ident: 30 – ident: 25 doi: 10.1016/B978-0-12-531680-4.50012-5 – ident: 16 doi: 10.1002/cpa.3160390607 – ident: 6 – ident: #cr-split#-23.2 – ident: 27 – ident: 1 doi: 10.1002/cpa.3160060402 – ident: 10 doi: 10.1512/iumj.1992.41.41005 |
| SSID | ssj0012962 |
| Score | 1.8835893 |
| Snippet | For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an associated Lagrangian,... For partial differential equations of mixed elliptic-hyperbolic and degenerate types which are the Euler-Lagrange equations for an associated Lagrangian,... |
| SourceID | projecteuclid crossref istex |
| SourceType | Open Access Repository Aggregation Database Publisher |
| StartPage | 251 |
| SubjectTerms | 35A05 35B33 35L65 35M10 58J70 Conservation laws Critical exponents Equations of mixed type Invariance and symmetry properties [See also 35A30] |
| Title | Conservation laws for equations of mixed elliptic-hyperbolic and degenerate types |
| URI | https://api.istex.fr/ark:/67375/765-1302DRD4-1/fulltext.pdf http://projecteuclid.org/euclid.dmj/1111609852 |
| Volume | 127 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://sdu.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwtV3Pb9MwFLbKdoHDxE8x2JAPiMvkkthOHB-ntWhiMMG6StwiJ3bGYG23thHjv9-znTopG9I4cEkrq6mt9z4_v-f3_Bmht9JkVBoWkyqlBeGqKInSKiay4ipVOpE-o3s4EsffssGQD3u9VbF72_ZfNQ1toGt7cvYftB3-FBrgO-gcnqB1eN5L7_YGztVG696F-rXwpN5XdVvzNjm_BjfTMnGCvSjJdwhF54XlB3aZBG3OHBX10rj92UXXfXW1HJPA9NoyT4S6nvpy1p5cDyb_i_rtd06PYB2e7p301zYbkk6NiqsYGR8Nbx1h7JrXGNz1yN9a3DeNReWCCOavmg4m1_MBNNiiXQPa0M_6tZj6q0RvmXnPiDEK_RFHviggrs7adW2Vy_9juQtFiGr-01a1iSQXaWLTenRwMuA5hNKbFKyWNZqjj8chJUVl6qnnmz6b42AwlPd3DmTN0dm0c_baFt76_TVTlxfnuuPJnD5GW00Igvc9dp6gnpk-RY8-B60unqGvXRRhiyIMKMIBRXhWYYcifAeKMKAItyjCDkXP0fjD8PTgkDSXb5CS8WxJqkxmVVVYOqBCSkPBjVZVWRQiiZmgZZUlXBkmuCy5igrwAnUCc5xlVBsRcU3ZC7QxnU3NS4QNFzSumDBxGvGCMsUULbXSWUKZBBd1G_VXksovPcdKbmNTEG3uRJtb0eYR6MaKNocX3jl5hl__TZXbSK4JPLxgSdUPxp-a1uZDT364gDiNJAzt1X07eY0etlNlB20s57XZRQ8Wun7jEHQD8SmSGw |
| link.rule.ids | 230,315,782,786,887,27933,27934 |
| linkProvider | Multiple Vendors |
| 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=Conservation+laws+for+equations+of+mixed+elliptic-hyperbolic+and+degenerate+types&rft.jtitle=Duke+mathematical+journal&rft.au=Lupo%2C+Daniela&rft.au=Payne%2C+Kevin+R.&rft.date=2005-04-01&rft.pub=DUKE+University+Press&rft.issn=0012-7094&rft.eissn=1547-7398&rft.volume=127&rft.issue=2&rft.spage=251&rft.epage=290&rft_id=info:doi/10.1215%2FS0012-7094-04-12722-8&rft.externalDBID=n%2Fa&rft.externalDocID=ark_67375_765_1302DRD4_1 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0012-7094&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0012-7094&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0012-7094&client=summon |