33 citations · 58 across the 8 of their papers we have counts for
7 papers · 1 filter
Semilinear Neumann boundary value problems for measure-valued maps
Aleksei Kroshnin, Hugo Lavenant, Dmitry Vorotnikov
We study the Wasserstein lift of nonlinear Poisson systems with inhomogeneous Neumann boundary conditions. We establish the existence of minimizers using new estimates involving th…
Hidden convexity in a problem of nonlinear elasticity
Nassif Ghoussoub, Young-Heon Kim, Hugo Lavenant +1
We study compressible and incompressible nonlinear elasticity variational problems in a general context. Our main result gives a sufficient condition for an equilibrium to be a glo…
New estimates on the regularity of the pressure in density-constrained Mean Field Games
Hugo Lavenant, Filippo Santambrogio
We consider variational Mean Field Games endowed with a constraint on the maximal density of the distribution of players. Minimizers of the variational formulation are equilibria f…
Dynamical Optimal Transport on Discrete Surfaces
Hugo Lavenant, Sebastian Claici, Edward Chien +1
We propose a technique for interpolating between probability distributions on discrete surfaces, based on the theory of optimal transport. Unlike previous attempts that use linear…
Harmonic mappings valued in the Wasserstein space
Hugo Lavenant
We propose a definition of the Dirichlet energy (which is roughly speaking the integral of the square of the gradient) for mappings mu : Omega -> (P(D), W\_2) defined over a subset…
Optimal density evolution with congestion: L infinity bounds via flow interchange techniques and applications to variational Mean Field Games
Hugo Lavenant, Filippo Santambrogio
We consider minimization problems for curves of measure, with kinetic and potential energy and a congestion penalization, as in the functionals that appear in Mean Field Games with…
Time-convexity of the entropy in the multiphasic formulation of the incompressible euler equation
Hugo Lavenant
We study the multiphasic formulation of the incompressible Euler equation introduced by Brenier: infinitely many phases evolve according to the compressible Euler equation and are…