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Partial W2,p regularity for optimal transport maps

Chen, Shibing; Figalli, Alessio


We prove that, in the optimal transportation problem with general costs and positive continuous densities, the potential function is always of class W2,ploc for any p ≥ 1 outside of a closed singular set of measure zero. We also establish global W2,p estimates when the cost is a small perturbation of the quadratic cost. The latter result is new even when the cost is exactly the quadratic cost

CollectionsANU Research Publications
Date published: 2017
Type: Journal article
Source: Journal of Functional Analysis
DOI: 10.1016/j.jfa.2017.02.025


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