Free boundary partial regularity in the thin obstacle problem

Abstract

For the thin obstacle problem in ${\mathbb{R}}^n$, $n\ge 2$, we prove that at all free boundary points, with the exception of a $(n-3)$-dimensional set, the solution differs from its blow-up by higher order corrections. This expansion entails a $C^{1,1}$-type free boundary regularity result, up to a codimension 3 set.

References in corpus (2)

• Direct epiperimetric inequalities for the thin obstacle problem and applications
• Half-space solutions with $7/2$ frequency in the thin obstacle problem

Cited by in corpus (1)

• Integro-Differential Elliptic Equations