Published Paper
Inserted: 6 mar 2017
Last Updated: 17 dec 2018
Journal: Archive for Rational Mechanics and Analysis
Volume: 230
Pages: 125--184
Year: 2018
Notes:
A correction to this article is available online at https:/doi.org10.1007s00205-018-1273-x.
Abstract:
We provide a thorough description of the free boundary for the lower dimensional obstacle problem in $\mathbb{R}^{n+1}$ up to sets of null $\mathcal{H}^{n-1}$ measure. In particular, we prove
(i) local finiteness of the $(n-1)$-dimensional Hausdorff measure of the free boundary;
(ii) $\mathcal{H}^{n-1}$-rectifiability of the free boundary,
(iii) classification of the frequencies up to a set of dimension at most $(n-2)$ and classification of the blow-ups at $\mathcal{H}^{n-1}$ almost every free boundary point.
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