5 papers · 1 filter
A Dacorogna-Moser construction of transport maps on with application to geodesics on the space of couplings
Louis-Pierre Chaintron, Matteo Picco
A seminal work by Dacorogna and Moser introduced a way of constructing regular transport maps from a probability distribution on a bounded domain to another one. In this work, we e…
Geodesic convexity and strengthened functional inequalities in submanifolds of Wasserstein space
Louis-Pierre Chaintron, Daniel Lacker
We study the geodesic convexity of various energy and entropy functionals restricted to (non-geodesically convex) submanifolds of Wasserstein spaces with their induced geometry. We…
Propagation of weak log-concavity along generalised heat flows via Hamilton-Jacobi equations
Louis-Pierre Chaintron, Giovanni Conforti, Katharina Eichinger
A well-known consequence of the Pr{é}kopa-Leindler inequality is the preservation of logconcavity by the heat semigroup. Unfortunately, this property does not hold for more genera…
Optimal rate of convergence in the vanishing viscosity for uniformly convex Hamilton-Jacobi equations
Louis-Pierre Chaintron, Samuel Daudin
The purpose of this note is to provide an optimal rate of convergence in the vanishing viscosity regime for first-order Hamilton-Jacobi equations with uniformly convex Hamiltonian.…
Optimal rate of convergence in the vanishing viscosity for quadratic Hamilton-Jacobi equations
Louis-Pierre Chaintron, Samuel Daudin
The purpose of this note is to provide an optimal rate of convergence in the vanishing viscosity regime for first-order Hamilton-Jacobi equations with purely quadratic Hamiltonian.…