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Variational and viscosity operators for the evolutionary Hamilton–Jacobi equation

hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
hal.structure.identifierDépartement de Mathématiques et Applications - ENS Paris [DMA]
hal.structure.identifierUnité de Mathématiques Pures et Appliquées [UMPA-ENSL]
dc.contributor.authorRoos, Valentine
dc.date.accessioned2018-09-12T10:57:28Z
dc.date.available2018-09-12T10:57:28Z
dc.date.issued2018
dc.identifier.issn0219-1997
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/18005
dc.language.isoenen
dc.subjectHamilton–Jacobi equationen
dc.subjectvariational solutionen
dc.subjectviscosity solutionen
dc.subjectminmax selectoren
dc.subjectLax-Oleinik semigroupen
dc.subject.ddc515en
dc.titleVariational and viscosity operators for the evolutionary Hamilton–Jacobi equationen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe study the Cauchy problem for the first order evolutive Hamilton-Jacobi equation with a Lipschitz initial condition. The Hamiltonian is not necessarily convex in the momentum variable and not a priori compactly supported. We build and study an operator giving a variational solution of this problem, and get local Lipschitz estimates on this operator. Iterating this variational operator we obtain the viscosity operator and extend the estimates to the viscosity framework. We also check that the construction of the variational operator gives the Lax-Oleinik semigroup if the Hamiltonian is convex or concave in the momentum variable.en
dc.relation.isversionofjnlnameCommunications in Contemporary Mathematics
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages1-67en
dc.relation.isversionofdoi10.1142/S0219199718500189en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01637617en
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2018-07-26T12:55:56Z
hal.author.functionaut


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