Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.
The regularity of mappings with a convex potential.Journal of the American Mathematical Society, 5(1):99–104, 1992
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Stability of optimal transport maps and second variation of the 2-Monge-Kantorovich distance
Lipschitz L² stability estimates for OT maps in terms of 2-MK distance (and C^{1,α} under Hölder) plus explicit second variation of quadratic MK distance via Monge-Ampère linearization.