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arXiv · 1801.05523

On the multiple membranes problem

Ovidiu Savin·Hui Yu
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Abstract

We establish the optimal regularity for solutions to the multiple membranes problem, and perform a blow-up analysis at points on the free boundary with the highest multiplicity. This leads to a complete classification of blow-up profiles in the plane. The main technical tool is a Weiss-type monotonicity formula.

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Ovidiu Savin, Hui Yu. 2018-01-17. On the multiple membranes problem. https://arxiv.org/abs/1801.05523

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