Regularity of optimal mapping between hypercubes
Advanced Nonlinear Studies
In this note, we establish the global C3,α regularity for potential functions in optimal transportation between hypercubes in ℝn for n ≥ 3. When n = 2, the result was proved by Jhaveri. The C3,α regularity is also optimal due to a counterexample in the study by Jhaveri.
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Australian Research Council