Geometric linearisation for optimal transport with strongly p-convex cost
arXiv:2303.10760
Abstract
We prove a geometric linearisation result for minimisers of optimal transport problems where the cost-function is strongly p-convex and of p-growth. Initial and target measures are allowed to be rough, but are assumed to be close to Lebesgue measure.
Final version as published in Calc. Var. Part. Differ. Equat. 63