We have created a functional framework for a class of non-metric gradient systems. The
state space is a space of nonnegative measures, and the class of systems includes the …

We investigate a first-order mean field planning problem of the form {−∂ t u+ H (x, D u)= f (x,
m) in (0, T)× R d,∂ tm−∇⋅(m H p (x, D u))= 0 in (0, T)× R d, m (0,⋅)= m 0, m (T,⋅)= m T in R …

We demonstrate the versatility of mean-field games (MFGs) as a mathematical framework for
explaining, enhancing, and designing generative models. In generative flows, a Lagrangian …

We present a variational reformulation of a class of doubly nonlinear parabolic equations as
(limits of) constrained convex minimization problems. In particular, an ε-dependent family of …

For two classes of Mean Field Game systems we study the convergence of solutions as the
interest rate in the cost functional becomes very large, modelling agents caring only about a …

The p-Laplacian evolution equation in metric measure spaces has been studied as the
gradient flow in L 2 of the p-Cheeger energy (for 1< p<∞). In this paper, using the first-order …

In this work we give optimal, ie, necessary and sufficient, conditions for integrals of the
calculus of variations to guarantee the existence of solutions---both weak and variational …

We present a novel variational view at Lagrangian mechanics based on the minimization of
weighted inertia-energy functionals on trajectories. In particular, we introduce a family of …

The sliced Wasserstein metric compares probability measures on $\mathbb {R}^ d $ by
taking averages of the Wasserstein distances between projections of the measures to lines …

We prove uniform parabolic Hölder estimates of De Giorgi–Nash–Moser type for sequences
of minimizers of the functionals E ε (W)=∫ 0∞ et/ε ε {∫ R+ N+ 1 ya ε|∂ t W| 2+|∇ W| 2 d …