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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: $1/2,3/2,\dots,m-1/2,\ldots$
Keywords:
Signorini problem, thin obstacle problem, thin free boundary, optimal regularity, contact with fixed boundary, Almgren's frequency formula.
Received: 12.01.2015
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
Linking options:
https://www.mathnet.ru/eng/aa1440 https://www.mathnet.ru/eng/aa/v27/i3/p183
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Abstract page: | 220 | Full-text PDF : | 50 | References: | 32 | First page: | 12 |
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