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Algebra i Analiz, 2015, Volume 27, Issue 3, Pages 183–201 (Mi aa1440)  

Research Papers

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

N. Matevosyana, A. Petrosyanb

a Department of Mathematics, University of Texas at Austin, Austin, TX 78712, USA
b Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA

Abstract: 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: $1/2,3/2,…,m-1/2,\ldots$

Keywords: Signorini problem, thin obstacle problem, thin free boundary, optimal regularity, contact with fixed boundary, Almgren's frequency formula.

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English version:
St. Petersburg Mathematical Journal, 2016, 27:3, 481–494

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Received: 12.01.2015
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Citation: N. Matevosyan, A. Petrosyan, “Contact of a thin free boundary with a fixed one in the Signorini problem”, Algebra i Analiz, 27:3 (2015), 183–201; St. Petersburg Math. J., 27:3 (2016), 481–494

Citation in format AMSBIB
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