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The interior Euler-Lagrange operator in field theory
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| dc.title | The interior Euler-Lagrange operator in field theory | en |
| dc.contributor.author | Volná, Jana | |
| dc.contributor.author | Urban, Zbyněk | |
| dc.relation.ispartof | Mathematica Slovaca | |
| dc.identifier.issn | 0139-9918 Scopus Sources, Sherpa/RoMEO, JCR | |
| dc.date.issued | 2016 | |
| utb.relation.volume | 65 | |
| utb.relation.issue | 6 | |
| dc.citation.spage | 1427 | |
| dc.citation.epage | 1444 | |
| dc.type | article | |
| dc.language.iso | en | |
| dc.publisher | Walter De Gruyter Gmbh | |
| dc.identifier.doi | 10.1515/ms-2015-0097 | |
| dc.relation.uri | http://www.lepageri.eu/files/preprints/VolnaUrban-LRIPreprint2013-1.pdf | |
| dc.subject | interior Euler-Lagrange operator | en |
| dc.subject | jet | en |
| dc.subject | Lagrangian | en |
| dc.subject | Euler-Lagrange expressions | en |
| dc.subject | Helmholtz conditions | en |
| dc.subject | variational sequence | en |
| dc.description.abstract | The paper is devoted to the interior Euler-Lagrange operator in field theory, representing an important tool for constructing the variational sequence. We give a new invariant definition of this operator by means of a natural decomposition of spaces of differential forms, appearing in the sequence, which defines its basic properties. Our definition extends the well-known cases of the Euler-Lagrange class (Euler-Lagrange form) and the Helmholtz class (Helmholtz form). This linear operator has the property of a projector, and its kernel consists of contact forms. The result generalizes an analogous theorem valid for variational sequences over 1-dimensional manifolds and completes the known heuristic expressions by explicit characterizations and proofs. (C) 2015 Mathematical Institute Slovak Academy of Sciences | en |
| utb.faculty | Faculty of Applied Informatics | |
| dc.identifier.uri | http://hdl.handle.net/10563/1006328 | |
| utb.identifier.rivid | RIV/70883521:28140/15:63524585!RIV20-MSM-28140___ | |
| utb.identifier.obdid | 43881162 | |
| utb.identifier.scopus | 2-s2.0-84958953802 | |
| utb.identifier.wok | 000372199300014 | |
| utb.source | j-wok | |
| dc.date.accessioned | 2016-06-22T12:14:47Z | |
| dc.date.available | 2016-06-22T12:14:47Z | |
| dc.description.sponsorship | Ministry of Education, Youth and Sports of the Czech Republic [CZ.1.07/2.3.00/30.0058] | |
| utb.contributor.internalauthor | Volná, Jana | |
| utb.fulltext.affiliation | Jana Volná, Zbyněk Urban Department of Mathematics, Faculty of Applied Informatics, Tomas Bata University in Zlin Nad Stranemi 4511, 760 05 Zlin, Czech Republic e-mail: volna@fai.utb.cz Lepage Research Institute, 783 42 Slatinice, Czech Republic e-mail: zbynek.urban@lepageri.eu | |
| utb.fulltext.dates | - | |
| utb.fulltext.references | [1] ANDERSON, I. M.: Introduction to the variational bicomplex, Contemporary Math. 132 (1992), 51–73. [2] BAUDERON, M.: Le probleme inverse du calcul des variations, Ann. Inst. H. Poincare, A 36 (1982), 159–179. [3] DEDECKER P.—TULCZYJEW, W. M.: Spectral sequences and the inverse problem of the calculus of variations. In: Diff. Geom. Methods in Math. Phys., Proc. Conf., Aix-en-Provence and Salamanca 1979, Lecture Notes in Math. 836 (1980), 498–503. [4] KRBEK, M.—MUSILOVÁ, J.: Representation of the Variational Sequence by Differential Forms, Acta Appl. Math. 88 (2005), 177–199. [5] KRUPKA, D.: Some Geometric Aspects of Variational Problems in Fibred Manifolds, Folia Fac. Sci. Nat. Univ. Purk. Brunensis, Physica, XIV, Brno, Czechoslovakia, 1973, pp. 65., arXiv:mathph/0110005. [6] KRUPKA, D.: Variational sequences on finite order jet spaces. In: Diff. Geom. Appl., Proc. Conf., Brno, Czechoslovakia, August 1989 (J. Janyska and D. Krupka, eds.), World Scientific, Singapore, 1990, pp. 236–254. [7] KRUPKA, D.: Variational sequences in mechanics, Calc. Var. 5 (1997), 557–583. [8] KRUPKA, D.—ŠEDĚNKOVÁ, J.: Variational sequences and Lepage forms. In: Diff. Geom. Appl., Proc. Conf., Prague, August 2004 (J. Bures, O. Kowalski and D. Krupka, eds.), Charles University, Prague, Czech Republic, 2005, pp. 617–627. [9] KRUPKA, D.: Global variational theory in fibred spaces. In: Handbook of Global Analysis (D. Krupka and D. Saunders, eds.) Elsevier, Amsterdam, 2007, pp 773–836. [10] MIKULSKI, W. M.: Uniqueness results for operators in the variational sequence, Ann. Pol. Math. 95, No. 2 (2009) 125–133. [11] ŠEDĚNKOVÁ, J.: On the invariant variational sequences in mechanics, Rend. Circ. Mat. Palermo, Proc. of the 22nd Winter School Geom. and Phys., Srni, January 2002; Ser. II, 71 (2003) 185–190. [12] ŠEDĚNKOVÁ, J.: Representations of variational sequences and Lepage forms, Ph.D. Thesis, Palacky University, Olomouc, 2004. [13] VOLNÁ, J.: Interior Euler-Lagrange operator, Preprint Series in Global Analysis and Applications, Palacky University, Olomouc, 6 (2005) 1–9. [14] VITOLO, R.: Variational sequences. In: Handbook of Global Analysis (D. Krupka and D. Saunders, eds.) Elsevier, Amsterdam, 2007, pp. 1115–1163. | |
| utb.fulltext.sponsorship | - | |
| utb.fulltext.projects | - | |
| utb.fulltext.faculty | Faculty of Applied Informatics | |
| utb.fulltext.ou | Department of Mathematics |
