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

Authors: N. Matevosyan and A. Petrosyan
Original publication: Algebra i Analiz, tom 27 (2015), nomer 3.
Journal: St. Petersburg Math. J. 27 (2016), 481-494
MSC (2010): Primary 35R35
Published electronically: March 30, 2016
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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 \geq 3/2$, while at the noncontact points the homogeneity must take one of the values: $ 1/2, 3/2,\dots ,m-1/2,\dots $.

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Additional Information

N. Matevosyan
Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712

A. Petrosyan
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Keywords: Signorini problem, thin obstacle problem, thin free boundary, optimal regularity, contact with fixed boundary, Almgren's frequency formula
Received by editor(s): January 12, 2015
Published electronically: March 30, 2016
Additional Notes: The first author was supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST)
The second author was supported in part by NSF grant DMS-1101139
Dedicated: Dedicated to N. N. Ural’tseva on the occasion of her 80th birthday
Article copyright: © Copyright 2016 American Mathematical Society