Contact of a thin free boundary with a fixed one in the Signorini problem
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- by N. Matevosyan and A. Petrosyan
- St. Petersburg Math. J. 27 (2016), 481-494
- DOI: https://doi.org/10.1090/spmj/1399
- 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: $1/2, 3/2,\dots ,m-1/2,\dots$.References
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Bibliographic Information
- N. Matevosyan
- Affiliation: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
- Email: nmatevosyan@math.utexas.edu
- A. Petrosyan
- Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
- MR Author ID: 654444
- Email: arshak@math.purdue.edu
- 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 - © Copyright 2016 American Mathematical Society
- Journal: St. Petersburg Math. J. 27 (2016), 481-494
- MSC (2010): Primary 35R35
- DOI: https://doi.org/10.1090/spmj/1399
- MathSciNet review: 3570962
Dedicated: Dedicated to N. N. Ural’tseva on the occasion of her 80th birthday