00496nas a2200109 4500008004100000245017800041210006900219260001800288100002100306700002300327856003600350 2003 en d00aAutonomous integral functionals with discontinous nonconvex integrands: Lipschitz regularity of mimimizers, DuBois-Reymond necessary conditions and Hamilton-Jacobi equations0 aAutonomous integral functionals with discontinous nonconvex inte bSISSA Library1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/162501109nas a2200121 4500008004100000245009500041210006900136260001800205520068400223100002100907700002300928856003600951 2001 en d00aUniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations0 aUniqueness of solutions to HamiltonJacobi equations arising in t bSISSA Library3 aWe prove the uniqueness of the viscosity solution to the Hamilton-Jacobi equation associated with a Bolza problem of the Calculus of Variations, assuming that the Lagrangian is autonomous, continuous, superlinear, and satisfies the usual convexity hypothesis. Under the same assumptions we prove also the uniqueness, in a class of lower semicontinuous functions, of a slightly different notion of solution, where classical derivatives are replaced only by subdifferentials. These results follow from a new comparison theorem for lower semicontinuous viscosity supersolutions of the Hamilton-Jacobi equation, that is proved in the general case of lower semicontinuous Lagrangians.1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/151500421nas a2200109 4500008004100000245010300041210006900144260001800213100002100231700002300252856003600275 2000 en d00aValue Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi inequalities0 aValue Functions for Bolza Problems with Discontinuous Lagrangian bSISSA Library1 aDal Maso, Gianni1 aFrankowska, Helene uhttp://hdl.handle.net/1963/1514