01109nas 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/1963/1515