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arXiv · 2112.11104

Free boundary partial regularity in the thin obstacle problem

Federico Franceschini·Joaquim Serra
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Abstract

For the thin obstacle problem in $\mathbb{R}^n$, $n\geq 2$, 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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Federico Franceschini, Joaquim Serra. 2021-12-21. Free boundary partial regularity in the thin obstacle problem. https://doi.org/10.1002/cpa.22152

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