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In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument, using a recent global regularity of optimal transportation in convex domains by the authors.

In this note, we establish the global C3,α{C}^{3,\alpha }regularity for potential functions in optimal transportation between hypercubes in Rn{{\mathbb{R}}}^{n}for n≥3n\ge 3. When n=2n=2, the result was proved by Jhaveri. The C3,α{C}^{3,\alpha }regularity is also optimal due to a counterexample in the study by Jhaveri.

Objective/Hypothesis:Local treatment of the cochlea after electrode insertion trauma with dexamethasone base conserves hearing against trauma‐induced loss.

Polymer-eluted dexamethasone (DXM) will retain its ability to protect against tumor necrosis factor (TNF)-induced hair cell (HC) loss.