Fitxers
Tipus de document
ArticleVersió
Versió acceptadaData de publicació
Tots els drets reservats
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/194135
Generic regularity of free boundaries for the obstacle problem
Títol de la revista
Director/Tutor
Contribució addicional
ISSN de la revista
Títol del volum
Resum
The goal of this paper is to establish generic regularity of free boundaries for the obstacle problem in $\mathbb{R}^n$. 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 $(n-1)$-dimensional - that is, as large as the regular set. Our main result establishes that, generically, the singular set has zero $\mathcal{H}^{n-4}$ measure (in particular, it has codimension 3 inside the free boundary). In particular, for $n \leq 4$, the free boundary is generically a $C^{\infty}$ manifold. This solves a conjecture of Schaeffer (dating back to 1974 ) on the generic regularity of free boundaries in dimensions $n \leq 4$
Recurs relacionat
Citació
Citació
FIGALLI, Alessio, ROS, Xavier and SERRA MONTOLÍ, Joaquim. Generic regularity of free boundaries for the obstacle problem. Publications mathématiques de l'IHÉS. 2020. Vol. 132, num. 1, pags. 181-292. ISSN 0073-8301. [consulted: 29 of September of 2026]. Available at: https://hdl.handle.net/2445/194135