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math.AP2023
A comparison principle for semilinear Hamilton-Jacobi-Bellman equations in the Wasserstein space
Samuel Daudin, Benjamin Seeger
The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton-Jacobi equations in the space of probability measures. The method involves…
math.AP2023
Linear and nonlinear transport equations with coordinate-wise increasing velocity fields
Pierre-Louis Lions, Benjamin Seeger
We consider linear and nonlinear transport equations with irregular velocity fields, motivated by models coming from mean field games. The velocity fields are assumed to increase i…
math.AP2023
Transport equations and flows with one-sided Lipschitz velocity fields
Pierre-Louis Lions, Benjamin Seeger
We study first- and second-order linear transport equations, as well as ODE and SDE flows, with velocity fields satisfying a one-sided Lipschitz condition. Depending on the time di…