[Turnpike theorem and the Hamilton–Jacobi equation]
For a problem of calculus of variations in infinite horizon, linear with respect to the derivative, we use the viscosity solutions theory to obtain a unique characterization of the value function by an Hamilton–Jacobi equation. This approach allows to extend in the scalar case a known result of turnpike property.
Pour un problème de calcul des variations en horizon infini, linéaire en la dérivée, nous utilisons la théorie des solutions de viscosité pour obtenir une caractérisation univoque de la fonction valeur à l'aide d'une équation d'Hamilton–Jacobi. Cette approche permet d'étendre pour le cas scalaire un résultat connu sous le nom de théorème de l'autoroute.
Accepted:
Published online:
Alain Rapaport 1; Pierre Cartigny 2
@article{CRMATH_2002__335_12_1091_0, author = {Alain Rapaport and Pierre Cartigny}, title = {Th\'eor\`eme de l'autoroute et \'equation {d'Hamilton{\textendash}Jacobi}}, journal = {Comptes Rendus. Math\'ematique}, pages = {1091--1094}, publisher = {Elsevier}, volume = {335}, number = {12}, year = {2002}, doi = {10.1016/S1631-073X(02)02613-4}, language = {fr}, }
Alain Rapaport; Pierre Cartigny. Théorème de l'autoroute et équation d'Hamilton–Jacobi. Comptes Rendus. Mathématique, Volume 335 (2002) no. 12, pp. 1091-1094. doi : 10.1016/S1631-073X(02)02613-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02613-4/
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