科研之友
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摘要
We prove some interior regularity results for potential functions of optimal transportation problems with power costs. The main point is that our problem is equivalent to a new optimal transportation problem whose cost function is a sufficiently small perturbation of the quadratic cost, but it does not satisfy the well known condition (A.3) guaranteeing regularity. The proof consists in a perturbation argument from the standard Monge-AmpSre equation in order to obtain, first, interior C-1,C-1 estimates for the potential and, second, interior Holder estimates for second derivatives. In particular, we take a close look at the geometry of optimal transportation when the cost function is close to quadratic in order to understand how the equation degenerates near the boundary.
- 出版日期2014-5
