36 citations · 125 across the 24 of their papers we have counts for
3 papers · 1 filter
Almost sharp rates of convergence for the average cost and displacement in the optimal matching problem
Michael Goldman, Martin Huesmann, Felix Otto
In this note we prove estimates for the average cost in the quadratic optimal transport problem on the two-dimensional flat torus which are optimal up to a double logarithm. We als…
Quantitative linearization results for the Monge-Ampère equation
Michael Goldman, Martin Huesmann, Felix Otto
This paper is about quantitative linearization results for the Monge-Ampère equation with rough data. We develop a large-scale regularity theory and prove that if a measure is…
A large-scale regularity theory for the Monge-Ampere equation with rough data and application to the optimal matching problem
Michael Goldman, Martin Huesmann, Felix Otto
The aim of this paper is to obtain quantitative bounds for solutions to the optimal matching problem in dimension two. These bounds show that up to a logarithmically divergent shif…