
Journal of Convex Analysis 30 (2023), No. 2, 591614 Copyright Heldermann Verlag 2023 HamiltonJacobi Equation for State Constrained Bolza Problems with Discontinuous Time Dependence: a Characterization of the Value Function Julien Bernis Univ Brest, UMR CNRS 6205, Laboratoire de Mathématiques de Bretagne Atlantique, 29200 Brest, France julien.bernis@univbrest.fr Piernicola Bettiol Univ Brest, UMR CNRS 6205, Laboratoire de Mathématiques de Bretagne Atlantique, 29200 Brest, France piernicola.bettiol@univbrest.fr We consider a class of state constrained Bolza problems in which the integral cost is merely continuous w.r.t. the state variable, and the dynamics and the integral cost are allowed to have a discontinuous behaviour w.r.t. the time variable t in the following sense: although they have everywhere onesided limits in t, they are required to be continuous only for a.e. t. For this class of problems we establish conditions under which the Value Function is characterized as the unique viscosity solution in the class of lower semicontinuous functions to the associated HamiltonJacobi equation. We provide some illustrative examples including a "growth versus consumption" problem in neoclassical macroeconomics, one peculiarity of which is the presence of a fractional singularity w.r.t. the state variable. Keywords: Value function, HamiltonJacobi equation, Bolza problem, state constraints. MSC: 49J15, 49J21, 49L20, 49L25. [ Fulltextpdf (195 KB)] for subscribers only. 