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arXiv · 2002.10628

Free boundary regularity in the triple membrane problem

Ovidiu Savin·Hui Yu
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Abstract

We investigate the regularity of the free boundaries in the 3 elastic membranes problem. We show that the two free boundaries corresponding to the coincidence regions between consecutive membranes are $C^{1,\log}$-hypersurfaces near a regular intersection point. We also study two types of singular intersections. The first type of singular points are locally covered by a $C^{1,\alpha}$-hypersurface. The second type of singular points stratify and each stratum is locally covered by a $C^1$-manifold.

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Ovidiu Savin, Hui Yu. 2020-02-25. Free boundary regularity in the triple membrane problem. https://arxiv.org/abs/2002.10628

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