000148432 001__ 148432 000148432 005__ 20250117162507.0 000148432 0247_ $$2doi$$a10.1063/1.5004260 000148432 0248_ $$2sideral$$a101980 000148432 037__ $$aART-2017-101980 000148432 041__ $$aeng 000148432 100__ $$aLéon, M. de 000148432 245__ $$aHamilton-jacobi theory in multisymplectic classical field theories 000148432 260__ $$c2017 000148432 5060_ $$aAccess copy available to the general public$$fUnrestricted 000148432 5203_ $$aThe geometric framework for the Hamilton-Jacobi theory developed in the studies of Carinena et al. [Int. J. Geom. Methods Mod. Phys. 3(7), 1417-1458 (2006)], Carinena et al. [Int. J. Geom. Methods Mod. Phys. 13(2), 1650017 (2015)], and de Léon et al. [Variations, Geometry and Physics (Nova Science Publishers, New York, 2009)] is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms of these theories as a particular case of a more general problem, and the classical Hamilton-Jacobi equation for field theories is recovered from this geometrical setting. Particular and complete solutions to these problems are defined and characterized in several equivalent ways in both formalisms, and the equivalence between them is proved. The use of distributions in jet bundles that represent the solutions to the field equations is the fundamental tool in this formulation. Some examples are analyzed and, in particular, the Hamilton-Jacobi equation for non-autonomous mechanical systems is obtained as a special case of our results. 000148432 536__ $$9info:eu-repo/grantAgreement/ES/AGAUR/2009 SGR1338$$9info:eu-repo/grantAgreement/ES/DGA/E24-1$$9info:eu-repo/grantAgreement/EC/FP7/246981/EU/Geometric Mechanics/GEOMECH$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2011-15725-E$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2011-22585$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2013-42870-P$$9info:eu-repo/grantAgreement/ES/MINECO/SEV-2011-0087 000148432 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/ 000148432 590__ $$a1.165$$b2017 000148432 591__ $$aPHYSICS, MATHEMATICAL$$b31 / 55 = 0.564$$c2017$$dQ3$$eT2 000148432 592__ $$a0.644$$b2017 000148432 593__ $$aMathematical Physics$$c2017$$dQ2 000148432 593__ $$aStatistical and Nonlinear Physics$$c2017$$dQ3 000148432 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion 000148432 700__ $$aPrieto-Martinez, P. D. 000148432 700__ $$aRoman-Roy, N. 000148432 700__ $$0(orcid)0000-0003-0404-1427$$aVilariño, S. 000148432 773__ $$g58, 9 (2017), 092901 [44 pp]$$pJ. math. phys.$$tJOURNAL OF MATHEMATICAL PHYSICS$$x0022-2488 000148432 8564_ $$s475580$$uhttps://zaguan.unizar.es/record/148432/files/texto_completo.pdf$$yPreprint 000148432 8564_ $$s1312344$$uhttps://zaguan.unizar.es/record/148432/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint 000148432 909CO $$ooai:zaguan.unizar.es:148432$$particulos$$pdriver 000148432 951__ $$a2025-01-17-14:35:37 000148432 980__ $$aARTICLE