Comptes Rendus
Partial Differential Equations
Uniqueness to elliptic and parabolic Hamilton–Jacobi–Bellman equations with non-smooth boundary
Comptes Rendus. Mathématique, Volume 339 (2004) no. 8, pp. 555-560.

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:
Accepted:
Published online:
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/

[1] G. Barles Solutions de Viscosité des Equations de Hamilton–Jacobi, Math. Appl., vol. 17, Springer-Verlag, 1994

[2] G. Barles Nonlinear Neumann boundary conditions for quasilinear elliptic equations and applications, J. Differential Equations, Volume 154 (1999) no. 1, pp. 191-224

[3] G. Barles; R. Buckdahn; E. Pardoux Backward stochastic differential equations and integral-partial differential equations, Stochastics Stochastics Rep., Volume 60 (1997), pp. 57-83

[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

[5] G. Barles; E. Rouy A strong comparison result for the Bellman equation arising in stochastic exit time control problems and its applications, Comm. Partial Differential Equations, Volume 23 (1998) no. 11/12, pp. 1945-2033

[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

[8] M.A. Katsoulakis Viscosity solutions of second order fully nonlinear elliptic equations with state constraints, Indiana Univ. Math. J., Volume 43 (1994) no. 2, pp. 493-517

[9] N.V. Krylov Controlled Diffusion Processes, Springer-Verlag, Berlin, 1980

[10] P.-L. Lions Optimal control of diffusion processes and HJB equations part II: viscosity solutions and uniqueness, Comm. Partial Differential Equations, Volume 8 (1983), pp. 1229-1276

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