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arXiv · 1409.4114

Contact of a thin free boundary with a fixed one in the Signorini problem

Norayr Matevosyan·Arshak Petrosyan
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Abstract

We study the Signorini problem near a fixed boundary, where the solution is "clamped down" or "glued." We show that in general the solutions are at least $C^{1/2}$ regular and that this regularity is sharp. We prove that near the actual points of contact of the free boundary with the fixed one the blowup solutions must have homogeneity $κ\geq 3/2$, while at the non-contact points the homogeneity must take one of the values: $1/2, 3/2, \ldots, m-1/2, \ldots$.

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Norayr Matevosyan, Arshak Petrosyan. 2014-09-14. Contact of a thin free boundary with a fixed one in the Signorini problem. https://arxiv.org/abs/1409.4114

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