Karen Yeressian: A minimization problem with free boundary related to a cooperative system

In this talk, I will present our study of a minimum problem for a functional involving a vector valued function [1]. The minimisation problem is related to a cooperative system. Using an array of technical tools, from geometric analysis for the free boundaries, we reduce the problem to its scalar counterpart and hence conclude similar results as that of scalar problem. This can also be seen as the most novel part, that possibly can lead to further developments of free boundary regularity for systems.


References:
[1] Luis A. Caffarelli, Henrik Shahgholian, Karen Yeressian, A minimization problem with free boundary related to a cooperative system, 2016, submitted, preprint: arXiv:1608.07689[math.AP]