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Hölder estimates in space-time for viscosity solutions of Hamilton-Jacobi equations

dc.contributor.authorCannarsa, Piermarco
dc.contributor.authorCardaliaguet, Pierre
dc.date.accessioned2011-09-06T14:28:19Z
dc.date.available2011-09-06T14:28:19Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/6921
dc.language.isoenen
dc.subjectHamilton-Jacobi equationsen
dc.subjectviscosity solutionsen
dc.subjectHölder continuityen
dc.subjectdegenerate parabolic equationsen
dc.subjectreverse Hölder inequalitiesen
dc.subject.ddc515en
dc.titleHölder estimates in space-time for viscosity solutions of Hamilton-Jacobi equationsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIt is well-known that solutions to the basic problem in the calculus of variations may fail to be Lipschitz-continuous when the Lagrangian depends on t. Similarly, for viscosity solutions to time-dependent Hamilton-Jacobi equations one cannot expect Lipschitz bounds to hold uniformly with respect to the regularity of coefficients. This phenomenon raises the question whether such solutions satisfy uniform estimates in some weaker norm. We will show that this is the case for a suitable Hölder norm, obtaining uniform estimates in (x,t) for solutions to first- and second-order Hamilton-Jacobi equations. Our results apply to degenerate parabolic equations and require superlinear growth at infinity, in the gradient variables, of the Hamiltonian. Proofs are based on comparison arguments and representation formulas for viscosity solutions, as well as weak reverse Hölder inequalities.en
dc.relation.isversionofjnlnameCommunications on Pure and Applied Mathematics
dc.relation.isversionofjnlvol63en
dc.relation.isversionofjnlissue5en
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages590-629en
dc.relation.isversionofdoihttp://dx.doi.org/10.1002/cpa.20315en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00371681/fr/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherWileyen
dc.subject.ddclabelAnalyseen


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