In this paper we report on some classical and more recent results about representation formulas for generalized solutions of the evolution partial differential equation ut + H(x,Du) = 0 , (x, t) 2 IRN × (0,+1) (1.1) We consider here only the case where H = H(x, p) is a convex function with respect to the p variable. In this setting, representation formulas can be obtained by exploiting the well - known connection existing via convex duality between the Hamilton - Jacobi equation (1.1) with Calculus of Variations or, more generally, Optimal Control problems.
Representations of solutions of Hamilton-Jacobi equations / CAPUZZO DOLCETTA, Italo. - STAMPA. - 54(2003), pp. 74-90.
Representations of solutions of Hamilton-Jacobi equations
CAPUZZO DOLCETTA, Italo
2003
Abstract
In this paper we report on some classical and more recent results about representation formulas for generalized solutions of the evolution partial differential equation ut + H(x,Du) = 0 , (x, t) 2 IRN × (0,+1) (1.1) We consider here only the case where H = H(x, p) is a convex function with respect to the p variable. In this setting, representation formulas can be obtained by exploiting the well - known connection existing via convex duality between the Hamilton - Jacobi equation (1.1) with Calculus of Variations or, more generally, Optimal Control problems.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
