Geodesic
Contact of a~thin free boundary with a~fixed one in the Signorini problem
Algebra i analiz, Tome 27 (2015) no. 3, pp. 183-201.

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The Signorini problem is studied near a fixed boundary where the solution is “clamped down” or “glued”. It is shown that, in general, the solutions are at least $C^{1/2}$ regular and that this regularity is sharp. Near the actual points of contact of the free boundary with the fixed one, the blowup solutions are shown to have homogeneity $\kappa\geq3/2$, while at the noncontact points the homogeneity must take one of the values: $1/2,3/2,\dots,m-1/2,\ldots$
Keywords: Signorini problem, thin obstacle problem, thin free boundary, optimal regularity, contact with fixed boundary, Almgren's frequency formula. 
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N. Matevosyan; A. Petrosyan. Contact of a~thin free boundary with a~fixed one in the Signorini problem. Algebra i analiz, Tome 27 (2015) no. 3, pp. 183-201. http://geodesic.mathdoc.fr/item/AA_2015_27_3_a8/

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