@article {2001,
title = {Uniqueness of solutions to Hamilton-Jacobi equations arising in the Calculus of Variations},
journal = {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},
number = {SISSA;57/00/M},
year = {2001},
publisher = {SISSA Library},
abstract = {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.},
url = {http://hdl.handle.net/1963/1515},
author = {Gianni Dal Maso and Helene Frankowska}
}