Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit
数学专题报告
报告题目(Title)：Rectifiability and uniqueness of blow-ups for points with positive Alt-Caffarelli-Friedman limit
报告人(Speaker)：Robin Neumayer (Carnegie Mellon University)
地点(Place)：Zoom ID: 979 3708 6485，Passcode: 336205
时间(Time)：2023 年 3月 17 日(周五), 9：00—10：00
邀请人(Inviter)：熊金钢
报告摘要
The Alt-Caffarelli-Friedman (ACF) monotonicity formula is an important tool in the study of free boundary problems. More generally, given any pair of nonnegative subharmonic functions with disjoint positivity sets, the ACF formula provides information about the interface between the supports. In this talk we'll show that on the portion of the interface where the ACF formula is asymptotically positive forms an H^{n-1}-rectifiable set, and that the two functions have unique blowups at H^{n-1} almost every such point. This talk is based on joint work with Mark Allen and Dennis Kriventsov.
* This PDE seminar is co-organized with Tianling Jin at The Hong Kong University of Science and Technology. See the seminar webpage: https://www.math.hkust.edu.hk/~tianlingjin/PDEseminar.html
