Generic regularity of free boundaries for the obstacle problem

Abstract: The obstacle problem is the most classical and motivating example in the study of free boundary problems. A milestone in this context is the classical work of Caffarelli (Acta Math. 1977), in which he established for the first time the regularity of free boundaries in the obstacle problem, outside a certain set of singular points. A long-standing open question in the field asks to establish generic regularity results in this setting (e.g. to prove that for ``almost every solution'' there are no singular points). The goal of this talk is to present some new results in this context, proving in particular the generic regularity of free boundaries for the obstacle problem in $\R^3$. This is a joint work with A. Figalli and J. Serra.

analysis of PDEs

Audience: researchers in the topic

PDE seminar via Zoom