52 citations · 257 across the 43 of their papers we have counts for
8 papers · 1 filter
Mass splitting in the time-discrete generalized Euler equations and non-Monge solutions in multi-marginal optimal transport
Gero Friesecke
The time-discretized, spatially continuous generalized Euler equations are a prototype example of multi-marginal optimal transport, yet the question whether they exhibit mass-split…
Partial regularity of optimal transport with Coulomb cost
Gero Friesecke, Tobias Ried
We prove that for two-marginal optimal transport with Coulomb cost on , the optimal map is a diffeomorphism outside a closed set of Lebesgue measure zero pr…
A simple counterexample to the Monge ansatz in multi-marginal optimal transport, convex geometry of the set of Kantorovich plans, and the Frenkel-Kontorova model
Gero Friesecke
It is known from clever mathematical examples \cite{Ca10} that the Monge ansatz may fail in continuous two-marginal optimal transport (alias optimal coupling alias optimal assignme…
Breaking the curse of dimension in multi-marginal Kantorovich optimal transport on finite state spaces
G. Friesecke, D. Vögler
We present a new ansatz space for the general symmetric multi-marginal Kantorovich optimal transport problem on finite state spaces which reduces the number of unknowns from $\tbin…
Density functional theory and optimal transportation with Coulomb cost
Codina Cotar, Gero Friesecke, Claudia Klüppelberg
We present here novel insight into exchange-correlation functionals in density functional theory, based on the viewpoint of optimal transport. We show that in the case of two elect…
Semiclassical limit of quantum dynamics with rough potentials and well posedness of transport equations with measure initial data
Luigi Ambrosio, Alessio Figalli, Gero Friesecke +2
In this paper we study the semiclassical limit of the Schrödinger equation. Under mild regularity assumptions on the potential which include Born-Oppenheimer potential energy s…