Regularity of solutions to a contact problem
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- by Russell M. Brown, Zhongwei Shen and Peter Shi PDF
- Trans. Amer. Math. Soc. 350 (1998), 4053-4063 Request permission
Abstract:
We consider a variational inequality for the Lamé system which models an elastic body in contact with a rigid foundation. We give conditions on the domain and the contact set which allow us to prove regularity of solutions to the variational inequality. In particular, we show that the gradient of the solution is a square integrable function on the boundary.References
- Russell Brown, The mixed problem for Laplace’s equation in a class of Lipschitz domains, Comm. Partial Differential Equations 19 (1994), no. 7-8, 1217–1233. MR 1284808, DOI 10.1080/03605309408821052
- Russell M. Brown and Zhongwei Shen, Estimates for the Stokes operator in Lipschitz domains, Indiana Univ. Math. J. 44 (1995), no. 4, 1183–1206. MR 1386766, DOI 10.1512/iumj.1995.44.2025
- B.E.J. Dahlberg, C.E. Kenig, J. Pipher, and G. Verchota, Area integral estimates for higher order elliptic equations and systems on Lipschitz domains, Ann. Inst. Fourier (Grenoble) 47 (1997), 1425–1461.
- B. E. J. Dahlberg, C. E. Kenig, and G. C. Verchota, Boundary value problems for the systems of elastostatics in Lipschitz domains, Duke Math. J. 57 (1988), no. 3, 795–818. MR 975122, DOI 10.1215/S0012-7094-88-05735-3
- G. Duvaut and J.-L. Lions, Inequalities in mechanics and physics, Grundlehren der Mathematischen Wissenschaften, vol. 219, Springer-Verlag, Berlin-New York, 1976. Translated from the French by C. W. John. MR 0521262
- Georges Duvaut, Équilibre d’un solide élastique avec contact unilatéral et frottement de Coulomb, C. R. Acad. Sci. Paris Sér. A-B 290 (1980), no. 5, A263–A265 (French, with English summary). MR 564325
- J. Král, J. Lukeš, I. Netuka, and J. Veselý (eds.), Potential theory—surveys and problems, Lecture Notes in Mathematics, vol. 1344, Springer-Verlag, Berlin, 1988. MR 973877, DOI 10.1007/BFb0103340
- Jiří Jarušek, Contact problems with bounded friction coercive case, Czechoslovak Math. J. 33(108) (1983), no. 2, 237–261. MR 699024
- Jindřich Nečas, Jiří Jarušek, and Jaroslav Haslinger, On the solution of the variational inequality to the Signorini problem with small friction, Boll. Un. Mat. Ital. B (5) 17 (1980), no. 2, 796–811 (English, with Italian summary). MR 580559
- Elias M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970. MR 0290095
- Alberto Torchinsky, Real-variable methods in harmonic analysis, Pure and Applied Mathematics, vol. 123, Academic Press, Inc., Orlando, FL, 1986. MR 869816
- Gregory Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains, J. Funct. Anal. 59 (1984), no. 3, 572–611. MR 769382, DOI 10.1016/0022-1236(84)90066-1
Additional Information
- Russell M. Brown
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
- MR Author ID: 259097
- Email: rbrown@ms.uky.edu
- Zhongwei Shen
- Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
- MR Author ID: 227185
- Email: shenz@ms.uky.edu
- Peter Shi
- Affiliation: Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309-4401
- Email: pshi@oakland.edu
- Received by editor(s): December 30, 1996
- Additional Notes: The authors thank the NSF and the Commonwealth of Kentucky for support through the NSF-EPSCoR program and through the NSF Division of Mathematical Sciences.
- © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 4053-4063
- MSC (1991): Primary 35J50; Secondary 73T05
- DOI: https://doi.org/10.1090/S0002-9947-98-02205-3
- MathSciNet review: 1475678