Obstructions to regularity in the classical Monge problem

2013/11/22 by Colombo, Maria, Indrei, Emanuel
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC) #Probability (math.PR)

paper · doi:10.48550/arxiv.1311.5868

Abstract

We provide counterexamples to regularity of optimal maps in the classical Monge problem under various assumptions on the initial data. Our construction is based on a variant of the counterexample in \citeLSW to Lipschitz regularity of the monotone optimal map between smooth densities supported on convex domains.

Related

• Regularity in Monge's mass transfer problem
• Lack of regularity of the transport density in the monge problem
• Global regularity in the Monge-Ampère obstacle problem
• Boundary ε-regularity in optimal transportation
• Regularity Properties of Monotone Measure-preserving Maps