Partial W2,p regularity for optimal transport maps
Date
2017
Authors
Chen, Shibing
Figalli, Alessio
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Publisher
Academic Press
Abstract
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
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Source
Journal of Functional Analysis
Type
Journal article