Comptes Rendus
no. 8
Partial Differential Equations
Uniqueness to elliptic and parabolic Hamilton–Jacobi–Bellman equations with non-smooth boundary
[Unicité aux équations d'Hamilton–Jacobi–Bellman elliptiques et paraboliques avec frontière irrégulière.]

Présenté par : Pierre-Louis Lions

Sébastien Chaumont1
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.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.08.009
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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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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[4] G. Barles; J. Burdeau The Dirichlet problem for semilinear second-order degenerate elliptic equations and applications to stochastic exit time control problems, Comm. Partial Differential Equations, Volume 20 (1995) no. 1/2, pp. 129-178

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[6] G. Barles; P.E. Souganidis Convergence of approximation schemes for fully nonlinear second order equations, Asymptotic Anal., vol. 4, Elsevier, North-Holland, 1991, pp. 273-283

[7] M.G. Crandall; H. Ishii; P.-L. Lions User's guide to viscosity solutions of 2nd order PDE, Bull. Amer. Math. Soc., Volume 27 (1992) no. 1, pp. 1-67

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