摘要
距离平方函数是最优传输问题中最重要的成本函数之一,它在许多领域都有着重要的应用.本文简要介绍在该成本函数下的最优传输问题,包括解的存在性、正则性、部分正则性以及相关的自由边界问题.
Abstract
The squared distance function is one of the most important cost functions in optimal transport problem and has significant applications in many fields.In this paper,we briefly introduce the optimal transport problems under this cost function,including the existence,regularity,and partial regularity of solutions,as well as related free boundary problems.
基金项目
科技部重点研发计划(2022YFA1005400)
科技部重点研发计划(2020YFA0713100)
国家自然科学基金(12225111)
国家自然科学基金(12141105)
Australian Research Council(DP200101084)
Australian Research Council(DP230100499)
Australian Research Council(FT220100368)
维普
万方数据