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.

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• Some New Monotonicity Formulas and the Singular Set in the Lower Dimensional Obstacle Problem
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Cited by in corpus (1)

• Integro-Differential Elliptic Equations