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 -