Value Functions for Bolza Problems with Discontinuous Lagrangians and Hamilton-Jacobi Inequalities

G. Dal Maso, H. Frankowska

We investigate the value function of the Bolza problem of the Calculus of Variations $$ V (t,x)=\inf \{\int_{0}^{t} L (y(s),y'(s))ds + ϕ(y(t)) : y \in W^{1,1} (0,t; R^n) ; y(0)=x \…