Carathéodory theory and a priori estimates for continuity inclusions in the space of probability measures
DOI10.1016/j.na.2024.113595MaRDI QIDQ6603995
Benoît Bonnet-Weill, Hélène Frankowska
Publication date: 12 September 2024
Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)
optimal transportset-valued analysisPeano existence theoremcompactness and relaxationcontinuity inclusionsFilippov estimates
Set-valued set functions and measures; integration of set-valued functions; measurable selections (28B20) Nonlinear differential equations in abstract spaces (34G20) Ordinary differential inclusions (34A60) Applications of functional analysis to differential and integral equations (46N20) Optimal transportation (49Q22)
Cites Work
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- Existence and uniqueness of measure solutions for a system of continuity equations with non-local flow
- \{Euclidean, metric, and Wasserstein\} gradient flows: an overview
- Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations
- Semiconcave functions, Hamilton-Jacobi equations, and optimal control
- Transport equation and Cauchy problem for BV vector fields
- The topology of compact convergence on continuous function spaces
- Necessary optimality conditions for optimal control problems in Wasserstein spaces
- Ordinary differential equations, transport theory and Sobolev spaces
- A priori estimates for operational differential inclusions
- The heat equation on manifolds as a gradient flow in the Wasserstein space
- Applied functional analysis. Functional analysis, Sobolev spaces and elliptic differential equations
- Mean field games
- A new class of transport distances between measures
- The Wasserstein gradient flow of the Fisher information and the quantum drift-diffusion equation
- Optimal trajectories associated with a solution of the contingent Hamilton-Jacobi equation
- Measurable viability theorems and the Hamilton-Jacobi-Bellman equation
- Necessary conditions for free end-time, measurably time dependent optimal control problems with state constraints
- The Pontryagin Maximum Principle in the Wasserstein space
- Necessary optimality conditions for infinite dimensional state constrained control problems
- Handling congestion in crowd motion modeling
- Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes
- Optimal control of multiagent systems in the Wasserstein space
- Mean field games with state constraints: from mild to pointwise solutions of the PDE system
- Compatibility of state constraints and dynamics for multiagent control systems
- Semiconcavity and sensitivity analysis in mean-field optimal control and applications
- Lagrangian, Eulerian and Kantorovich formulations of multi-agent optimal control problems: equivalence and gamma-convergence
- Differential inclusions in Wasserstein spaces: the Cauchy-Lipschitz framework
- Superposition principle and schemes for measure differential equations
- A uniqueness result for the decomposition of vector fields in \(\mathbb{R}^d\)
- Optimal transport for applied mathematicians. Calculus of variations, PDEs, and modeling
- Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system
- Measure-theoretic models for crowd dynamics
- Measure differential equations
- Gradient flows for non-smooth interaction potentials
- Multiscale modeling of pedestrian dynamics
- Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
- THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
- Mean-Field Optimal Control
- Mean-field sparse optimal control
- A MACROSCOPIC CROWD MOTION MODEL OF GRADIENT FLOW TYPE
- Asymptotic Flocking Dynamics for the Kinetic Cucker–Smale Model
- Functional Analysis, Calculus of Variations and Optimal Control
- An augmented Lagrangian approach to Wasserstein gradient flows and applications
- Stability Analysis of Flock and Mill Rings for Second Order Models in Swarming
- Entropic Approximation of Wasserstein Gradient Flows
- Control to Flocking of the Kinetic Cucker--Smale Model
- Random Fixed Point Theorems for Measurable Multifunctions in Banach Spaces
- Weak Compactness in L 1 (μ, X)
- Some Characterizations of Optimal Trajectories in Control Theory
- Remarks on Weak Compactness in L1(μ,X)
- Survey of Measurable Selection Theorems
- The Variational Formulation of the Fokker--Planck Equation
- The Master Equation and the Convergence Problem in Mean Field Games
- Strong Local Minimizers in Optimal Control Problems with State Constraints: Second-Order Necessary Conditions
- Stochastic Optimal Control Problems with Control and Initial-Final States Constraints
- The Maximum Principle for an Optimal Solution to a Differential Inclusion with End Points Constraints
- Mean-field optimal control as Gamma-limit of finite agent controls
- Continuity equations and ODE flows with non-smooth velocity
- Weak Compactness in L 1 (μ, X)
- Hamiltonian ODEs in the Wasserstein space of probability measures
- Young measure, superposition and transport
- On Certain Questions in the Theory of Optimal Control
- Convergence of Entropic Schemes for Optimal Transport and Gradient Flows
- Optimal Transport
- Set-valued analysis
- Second-order sufficient conditions. II: Weak local minima in an optimal control problem with a general control constraint
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