Value functions and the Dirichlet problem for Isaacs equation in a smooth domain

DOI10.1090/S0002-9947-09-04732-1zbMath1186.49021MaRDI QIDQ5322884

Jay Kovats

Publication date: 23 July 2009

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

differential gameviscosity solutionsIsaacs equation

Mathematics Subject Classification ID

Differential games and control (49N70) 2-person games (91A05) Smoothness and regularity of solutions to PDEs (35B65) Nonlinear elliptic equations (35J60) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (12)

Zero-sum path-dependent stochastic differential games in weak formulation ⋮ On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations ⋮ On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains ⋮ On regularity properties and approximations of value functions for stochastic differential games in domains ⋮ Approximating the value functions for stochastic differential games with the ones having bounded second derivatives ⋮ Fundamental solutions of homogeneous fully nonlinear elliptic equations ⋮ On the second order derivatives of solutions of a special Isaacs equation ⋮ Generalized Hamilton--Jacobi--Bellman Equations with Dirichlet Boundary Condition and Stochastic Exit Time Optimal Control Problem ⋮ On the independence of the value function for stochastic differential games of the probability space ⋮ On the Continuity of Stochastic Exit Time Control Problems ⋮ Stochastic representations for solutions to parabolic Dirichlet problems for nonlocal Bellman equations ⋮ The minmax principle and $W^{2,p}$ regularity for solutions of the simplest Isaacs equations

Cites Work

• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• Another approach to the existence of value functions of stochastic differential games
• Interior \(C^{2,\alpha}\) regularity theory for a class of nonconvex fully nonlinear elliptic equations.
• ON CONTROLLED DIFFUSION PROCESSES WITH UNBOUNDED COEFFICIENTS
• On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's
• SOME NEW RESULTS IN THE THEORY OF CONTROLLED DIFFUSION PROCESSES
• Optimal Control of Stochastic Integrals and Hamilton–Jacobi–Bellman Equations. I
• Differential games for stochastic partial differential equations
• A representation formula and regularizing properties for viscosity solutions of second-order fully nonlinear degenerate parabolic equations
• Stochastic differential games and viscosity solutions of Isaacs equations
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