Geodesic
Hamilton-Jacobi Equation for State Constrained Bolza Problems with Discontinuous Time Dependence: a Characterization of the Value Function
Journal of convex analysis, Tome 30 (2023) no. 2, pp. 591-614
Cet article a éte moissonné depuis la source Heldermann Verlag

Voir la notice de l'article

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 one-sided 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 Hamilton-Jacobi equation. We provide some illustrative examples including a "growth versus consumption" problem in neo-classical macro-economics, one peculiarity of which is the presence of a fractional singularity w.r.t. the state variable.
Classification : 49J15, 49J21, 49L20, 49L25
Mots-clés : Value function, Hamilton-Jacobi equation, Bolza problem, state constraints 
@article{JCA_2023_30_2_JCA_2023_30_2_a9,
     author = {J. Bernis and P. Bettiol},
     title = {Hamilton-Jacobi {Equation} for {State} {Constrained} {Bolza} {Problems} with {Discontinuous} {Time} {Dependence:} a {Characterization} of the {Value} {Function}},
     journal = {Journal of convex analysis},
     pages = {591--614},
     year = {2023},
     volume = {30},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2023_30_2_JCA_2023_30_2_a9/}
}
TY  - JOUR
AU  - J. Bernis
AU  - P. Bettiol
TI  - Hamilton-Jacobi Equation for State Constrained Bolza Problems with Discontinuous Time Dependence: a Characterization of the Value Function
JO  - Journal of convex analysis
PY  - 2023
SP  - 591
EP  - 614
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/JCA_2023_30_2_JCA_2023_30_2_a9/
ID  - JCA_2023_30_2_JCA_2023_30_2_a9
ER  - 
%0 Journal Article
%A J. Bernis
%A P. Bettiol
%T Hamilton-Jacobi Equation for State Constrained Bolza Problems with Discontinuous Time Dependence: a Characterization of the Value Function
%J Journal of convex analysis
%D 2023
%P 591-614
%V 30
%N 2
%U http://geodesic.mathdoc.fr/item/JCA_2023_30_2_JCA_2023_30_2_a9/
%F JCA_2023_30_2_JCA_2023_30_2_a9
J. Bernis; P. Bettiol. Hamilton-Jacobi Equation for State Constrained Bolza Problems with Discontinuous Time Dependence: a Characterization of the Value Function. Journal of convex analysis, Tome 30 (2023) no. 2, pp. 591-614. http://geodesic.mathdoc.fr/item/JCA_2023_30_2_JCA_2023_30_2_a9/