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arXiv · 1703.00678

On the measure and the structure of the free boundary of the lower dimensional obstacle problem

Matteo Focardi·Emanuele Spadaro
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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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Matteo Focardi, Emanuele Spadaro. 2017-08-31. On the measure and the structure of the free boundary of the lower dimensional obstacle problem. https://doi.org/10.1007/s00205-018-1242-4

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