Abstract:In this talk, we introduce some recent regularity results of free boundary in optimal transportation. Particularly for higher order regularity, when densities are Hölder continuous and domains are C^2, uniformly convex, we obtain the free boundary is C^{2,alpha} smooth. We also consider another model case that the target consists of two disjoint convex sets, in which singularities of optimal transport mapping arise. Under similar assumptions, we show that the singular set of the optimal mapping is an (n-1)-dimensional C^{2,alpha} regular sub-manifold of R^n. These are based on a series of joint work with Shibing Chen and Xu-Jia Wang.
报告人: 刘佳堃2006年本科毕业于浙江大学，2010年在澳大利亚国立大学获得博士学位。2010-2013年在普林斯顿大学做博士后研究，2013年至今任职于澳大利亚卧龙岗大学。刘佳堃主要研究领域为非线性椭圆和抛物偏微分方程及其在几何和最优运输中的应用。
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