Lipschitz continuity and local semiconcavity for exit time problems with state constraints

DOI10.1016/j.jde.2007.10.020zbMath1225.49035OpenAlexW2081816057MaRDI QIDQ932837

Marco Castelpietra, Piermarco Cannarsa

Publication date: 11 July 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2007.10.020

zbMATH Keywords

state constraintsLipschitz continuityvalue functiontime optimal controlsemiconcavity

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Regularity of solutions in optimal control (49N60) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (7)

Nonsmooth mean field games with state constraints ⋮ Multipopulation Minimal-Time Mean Field Games ⋮ Lipschitz regularity of the minimum time function of differential inclusions with state constraints ⋮ On the extension of the solutions of Hamilton-Jacobi equations ⋮ Kinodynamic Control Systems and Discontinuities in Clearance ⋮ One-sided Perron differential inclusions ⋮ Minimal-time mean field games

Cites Work

• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Regularity of solution maps of differential inclusions under state constraints
• Lipschitz continuity of the value function in optimal control
• Semiconcavity of the value function for exit time problems with nonsmooth target
• Convexity properties of the minimum time function
• Filippov's and Filippov-Ważewski's theorems on closed domains
• Existence and uniqueness for dislocation dynamics with nonnegative velocity
• Dislocation dynamics: Short-time existence and uniqueness of the solution
• On the Bellman function for the time-optimal process problem
• An Approximation Scheme for the Minimum Time Function
• Interior sphere property of attainable sets and time optimal control problems
• Regularity of the Eikonal Equation with Neumann Boundary Conditions in the Plane: Application to Fronts with Nonlocal Terms
• Interior sphere property for level sets of the value function of an exit time problem
• Clarke's tangent cones and the boundaries of closed sets in Rn
• Nonlocal First-Order Hamilton–Jacobi Equations Modelling Dislocations Dynamics
• Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations
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