Solutions de viscosité

notion de solution faible intermédiaire entre solution classique et solution au sens des distributions

Wikipedia : Viscosity solution (EN)

BBP97

Backward Stochastic Differential Equations and Integral-Partial Differential Equations, G. Barles, R. Buckdahn and E. Pardoux, Stochastics and Stochastics Reports 60 (1997) 57-83

BB95

The Dirichlet Problem for Semilinear Second-Order Degenerate Elliptic Equations and Applications to Stochastic Exit Time Control Problems, G. Barles and J. Burdeau, Communications in Partial Differential Equations 20, 1&2 (1995) 129-178

BR98

A Strong Comparison Result for the Bellman Equation Arising in Stochastic Exit Time Control Problems and its Applications, G. Barles and E. Rouy, Communications in Partial Differential Equations 23, 11&12 (1998) 1945-2033

BS97

Convergence of Approximation Schemes for Fully Nonlinear Second Order Equations, G. Barles and P. E. Souganidis, Asymptotic Analysis 4 (1991) 273-283 (Elsevier Science Publishers B.V., North-Holland)

C02

Gestion optimale de bilan de compagnie d'assurance, S. Chaumont, PhD Thesis, Université Henri Poincaré Nancy I (2002)

K94

Viscosity Solutions of Second Order Fully Nonlinear Elliptic Equations with State Constraints, M. A. Katsoulakis, Indiana University Mathematics Journal 43, 2 (1994) 493-517

K80

Controlled Diffusion Processes, N. V. Krylov (1980) (Springer Verlag, Berlin)

: L83

Optimal Control of diffusion processes and HJB equations part II : Viscosity Solutions and Uniqueness, P.-L. Lions, Communications in Partial Differential Equations 8, 11 (1983) 1229-1276

B99

Nonlinear Neumann Boundary Conditions for Quasilinear Elliptic Equations and Applications, G. Barles, J. Differential Equations 154, 1 (1999) 191-224

Bibliography

1. Solutions de Viscosité des Equations de Hamilton-Jacobi, G. Barles, Mathématiques et Applications 17 (1994), (Springer Verlag)

2. User's guide to Viscosity Solutions of 2nd Order PDE, M.G. Crandall and H. Ishii and P.-L. Lions, Bulletin of the American Mathematical Society 27, 1 (1992) 1-67