Lipschitz continuity and semiconcavity properties of the value function of a stochastic control problem

DOI10.1007/s00030-010-0078-xzbMath1205.93162OpenAlexW2043536252MaRDI QIDQ607778

Marc Quincampoix, Rainer Buckdahn, Piermarco Cannarsa

Publication date: 3 December 2010

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-010-0078-x

zbMATH Keywords

viscosity solutionLipschitz continuitysemiconcavitystochastic optimal control problemregularity resultsHamilton-Jacobi-Bellman typenonlinear parabolic partial differential equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Degenerate parabolic equations (35K65) Optimal stochastic control (93E20) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Viscosity solutions to PDEs (35D40)

Related Items (4)

Deterministic mean field games with control on the acceleration ⋮ Multidimensional singular control and related Skorokhod problem: sufficient conditions for the characterization of optimal controls ⋮ Joint time-state generalized semiconcavity of the value function of a jump diffusion optimal control problem ⋮ Generalized semiconcavity of the value function of a jump diffusion optimal control problem

Cites Work

• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• Controlled Markov processes and viscosity solutions
• Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations
• On the regularity theory of fully nonlinear parabolic equations: II
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