A Linear Equation on the Set of Probability Vectors on Graphs
In this paper we investigate solutions to a linear Hamilton-Jacobi equations in the Wasserstein space of probability vectors on a finite simply connected graph. We prove that there exists a solution under the assumption that the initial value function $u_0:\mathcal{P}(G)\to\mathbb{R}$ is Fréchet continuously differentiable.
math.AP↗