The level-set formulation of motion by mean curvature is a degenerate parabolic equation. We show it can be interpreted as the value function of a deterministic two-person game. More precisely, we… (More)

We study a two-dimensional model for micromagnetics, which consists in an energy functional over S-valued vector fields. Bounded-energy configurations tend to be planar, except in small regions which… (More)

We study vortices for solutions of the perturbed Ginzburg-Landau equations ∆u + 1 ε2 u(1−|u|2) = fε where fε is estimated in L. We prove upper bounds for the GinzburgLandau energy in terms of ‖fε‖L2… (More)

We are concerned with Γ-convergence of gradient flows, which is a notion meant to ensure that if a family of energy functionals depending of a parameter Γ-converges, then the solutions to the… (More)

We study an evolution equation proposed by Chapman-Rubinstein-Schatzman as a mean-field model for the evolution of the vortex-density in a superconductor. We treat the case of a bounded domain where… (More)

It was proved in [1] that if p ≥ N N−2 with N ≥ 3, then (1) has no solution in the sense of distributions with u ∈ L(Ω). However, in some sense, the unique “natural solution” is u = 0. This has to be… (More)

We show that a broad class of fully-nonlinear second-order parabolic or elliptic PDE’s can be realized as the Hamilton-Jacobi-Bellman equations of deterministic two-person games. More precisely:… (More)

We prove a central limit theorem for the linear statistics of one-dimensional log-gases, or β-ensembles. We use a method based on a change of variables which allows to treat fairly general… (More)

We continue the study of [AS] on the Chapman-Rubinstein-Schatzman-E evolution model for superconductivity, viewed as a gradient flow on the space of measures equipped with the quadratic Wasserstein… (More)