TY - JOUR T1 - Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations JF - Optimal control and partial differential equations : in honour of professor Alain Bensoussan\\\'s 60th birthday / edited by José Luis Menaldi, Edmundo Rofman, and Agnès Sulem.,Amsterdam : IOS Press, 2001, p. 335-345 Y1 - 2001 A1 - Gianni Dal Maso A1 - Helene Frankowska AB - We 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. PB - SISSA Library UR - http://hdl.handle.net/1963/1515 U1 - 2648 U2 - Mathematics U3 - Functional Analysis and Applications ER -