The aim of this paper is to discuss convergence of pointed metric measure spaces in the
absence of any compactness condition. We propose various definitions, and show that all of …

Replacing positivity constraints by an entropy barrier is popular to approximate solutions of
linear programs. In the special case of the optimal transport problem, this technique dates …

We show that degenerate nonlinear diffusion equations can be asymptotically obtained as a
limit from a class of nonlocal partial differential equations. The nonlocal equations are …

We prove that the unique entropy solution to a scalar nonlinear conservation law with strictly
monotone velocity and nonnegative initial condition can be rigorously obtained as the large …

This paper focuses on the role of a government of a large population of interacting agents as
a meanfield optimal control problem derived from deterministic finite agent dynamics. The …

We provide a rigorous mathematical framework to establish the limit of a nonlocal model of
cell-cell adhesion system to a local model. When the parameter of the nonlocality goes to 0 …

This paper studies the derivation of the quadratic porous medium equation and a class of
cross-diffusion systems from nonlocal interactions. We prove convergence of solutions of a …

Strong compactness results for families of functions in seminormed nonnegative cones in
the spirit of the Aubin-Lions-Dubinskiĭ lemma are proven, refining some recent results in the …

Let X be a separable, complete metric space and P _ p (X) be the space of Borel probability
measures with finite moment of order p> 1, metrized by the Wasserstein distance. In this …

This paper addresses the Cauchy problem for the gradient flow equation in a Hilbert
space\[\begin {cases} u'(t)+\partial_ {\ell}\phi (u (t))\ni f (t) &\text {{\it ae}\in}(0, T), u (0) …