20230717 
11:2012:20 
20230717,11:2012:20  LH A (A2) 
0717 Morning Basic Science Lectures

Speaker 
Generic regularity of free boundaries for the obstacle problem The classical obstacle problem consists of finding the equilibrium position of an elastic membrane whose boundary is held fixed and which is constrained to lie above a given obstacle. By classical results of Caffarelli, the free boundary is $C^\infty$ outside a set of singular points. Explicit examples show that the singular set could be in general (n1)dimensional \emdash that is, as large as the regular set. In a recent paper with RosOton and Serra we show that, generically, the singular set has zero $H^{n4}$ measure (in particular, it has codimension three inside the free boundary), solving a conjecture of Schaeffer in dimension $n \leq 4$. The aim of this talk is to give an overview of these results.
