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dc.contributor.authorGomes, Diogo A.
dc.contributor.authorTerrone, Gabriele
dc.date.accessioned2015-08-03T11:14:30Z
dc.date.available2015-08-03T11:14:30Z
dc.date.issued2013-08-01
dc.identifier.citationGomes, D. A., & Terrone, G. (2013). The Mather problem for lower semicontinuous Lagrangians. Nonlinear Differential Equations and Applications NoDEA, 21(2), 167–217. doi:10.1007/s00030-013-0243-0
dc.identifier.issn10219722
dc.identifier.doi10.1007/s00030-013-0243-0
dc.identifier.urihttp://hdl.handle.net/10754/562896
dc.description.abstractIn this paper we develop the Aubry-Mather theory for Lagrangians in which the potential energy can be discontinuous. Namely we assume that the Lagrangian is lower semicontinuous in the state variable, piecewise smooth with a (smooth) discontinuity surface, as well as coercive and convex in the velocity. We establish existence of Mather measures, various approximation results, partial regularity of viscosity solutions away from the singularity, invariance by the Euler-Lagrange flow away from the singular set, and further jump conditions that correspond to conservation of energy and tangential momentum across the discontinuity. © 2013 Springer Basel.
dc.description.sponsorshipD. Gomes was partially supported by CAMGSD-LARSys through FCT-Portugal and by grants PTDC/MAT/114397/2009, UTAustin/MAT/0057/2008, and UTA-CMU/MAT/0007/2009.G.Terrone was supported by the UTAustin-Portugal partnership through the FCT post-doctoral fellowship SFRH/BPD/40338/2007, CAMGSD-LARSys through FCT Program POCTI - FEDER and by grants PTDC/MAT/114397/2009, UTAustin/MAT/0057/2008, and UTA-CMU/MAT/0007/2009.
dc.publisherSpringer Nature
dc.subjectAction minimizing measures
dc.subjectDiscontinuous Lagrangians
dc.subjectHamilton-Jacobi equations
dc.subjectViscosity solutions
dc.titleThe Mather problem for lower semicontinuous Lagrangians
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalNonlinear Differential Equations and Applications NoDEA
dc.contributor.institutionDepartamento de Matemática Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior Técnico, 1049-001 Lisboa, Portugal
kaust.personGomes, Diogo A.
dc.date.published-online2013-08-01
dc.date.published-print2014-04


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