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The structure of the free boundary for lower dimensional obstacle problems

I. Athanasopoulos·L. A. Caffarelli·S. Salsa
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Abstract

We study the regularity of the "free surface" in boundary obstacle problems. We show that near a non-degenerate point the free boundary is a $C^{1,α}$ $(n-2)$-dimensional surface in $\real^{n-1}$.

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I. Athanasopoulos, L. A. Caffarelli, S. Salsa. 2006-09-01. The structure of the free boundary for lower dimensional obstacle problems. https://arxiv.org/abs/math/0609031

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