Uniqueness to elliptic and parabolic Hamilton–Jacobi–Bellman equations with non-smooth boundary

Sébastien Chaumont

doi:10.1016/j.crma.2004.08.009

Partial Differential Equations

Uniqueness to elliptic and parabolic Hamilton–Jacobi–Bellman equations with non-smooth boundary

Presented by: Pierre-Louis Lions

Sébastien Chaumont ¹

¹ Institut Élie Cartan, université Henri Poincaré Nancy I, B.P. 239, 54506 Vandœuvre-lès-Nancy cedex, France

Comptes Rendus. Mathématique, Volume 339 (2004) no. 8, pp. 555-560.

Abstract
Résumé

In the framework of viscosity solutions, we give an extension of the strong comparison result for Hamilton–Jacobi–Bellman (HJB) equations with Dirichlet boundary conditions to the case of some non-smooth domains. In particular, it may be applied to parabolic problems on cylindrical domains.

Dans le cadre de la théorie des solutions de viscosité, on donne une extension du principe de comparaison fort pour l'équation d'Hamilton–Jacobi–Bellman (HJB) avec condition au bord de type Dirichlet au cas de certains domaines irréguliers. En particulier, ce résultat est applicable aux problèmes paraboliques posés dans des domaines cylindriques.

Received: 2004-04-24
Accepted: 2004-08-28
Published online: 2004-10-01

DOI: 10.1016/j.crma.2004.08.009

Author's affiliations:

Sébastien Chaumont ¹

¹ Institut Élie Cartan, université Henri Poincaré Nancy I, B.P. 239, 54506 Vandœuvre-lès-Nancy cedex, France

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     title = {Uniqueness to elliptic and parabolic {Hamilton{\textendash}Jacobi{\textendash}Bellman} equations with non-smooth boundary},
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Sébastien Chaumont. Uniqueness to elliptic and parabolic Hamilton–Jacobi–Bellman equations with non-smooth boundary. Comptes Rendus. Mathématique, Volume 339 (2004) no. 8, pp. 555-560. doi : 10.1016/j.crma.2004.08.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.08.009/

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