Equivalence between strict viscosity solution and viscosity solution in the Wasserstein space and regular extension of the Hamiltonian in \(L^2_{\mathbb{P}}\)

Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21) Optimal transportation (49Q22)

Cites Work

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Semiconcave functions, Hamilton-Jacobi equations, and optimal control
Hamilton-Jacobi equations in the Wasserstein space
Hamilton-Jacobi equations in infinite dimensions. I: Uniqueness of viscosity solutions
Hamilton-Jacobi equations in infinite dimensions. II: Existence of viscosity solutions
Hamilton-Jacobi equations in infinite dimensions. III
Mayer control problem with probabilistic uncertainty on initial positions
On differentiability in the Wasserstein space and well-posedness for Hamilton-Jacobi equations
Optimal control of multiagent systems in the Wasserstein space
Compatibility of state constraints and dynamics for multiagent control systems
Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: equivalence and gamma-convergence
Hamilton-Jacobi inequalities on a metric space
Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
On a class of first order Hamilton-Jacobi equations in metric spaces
Solutions to Hamilton-Jacobi equation on a Wasserstein space
Hamilton-Jacobi equations for controlled gradient flows: the comparison principle
DETERMINISTIC DIFFERENTIAL GAMES UNDER PROBABILITY KNOWLEDGE OF INITIAL CONDITION
Finite Dimensional Approximations of Hamilton–Jacobi–Bellman Equations for Stochastic Particle Systems with Common Noise
Dynamical Systems and Hamilton–Jacobi–Bellman Equations on the Wasserstein Space and their L² Representations

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