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Regularity of solutions to a contact problem
Author(s):
Russell
M.
Brown;
Zhongwei
Shen;
Peter
Shi
Journal:
Trans. Amer. Math. Soc.
350
(1998),
4053-4063.
MSC (1991):
Primary 35J50;
Secondary 73T05
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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:
- [Bro94]
- Russell M. Brown, The mixed problem for Laplace's equation in a class of Lipschitz domains, Comm. Partial Diff. Eqns. 19 (1994), 1217-1233. MR 95i:35059
- [BS95]
- Russell M. Brown and Zhongwei Shen, Estimates for Stokes operator in Lipschitz domains, Indiana Univ. Math. J. 44 (1995), 1183-1206. MR 97c:35152
- [DKPV]
- 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. CMP 98:07
- [DKV88]
- B.E.J. Dahlberg, C.E. Kenig, and G. Verchota, Boundary value problems for the systems of elastostatics in Lipschitz domains, Duke Math. J. 57 (1988), 795-818. MR 90d:35259
- [DL76]
- G. Duvaut and J.L. Lions, Inequalities in mechanics and physics, Grundlehren der mathematischen Wissenschaften, vol. 219, Springer Verlag, 1976. MR 58:25191
- [Duv80]
- G. Duvaut, Équilibre d'un solide élastique avec contact unilatéral et frottement de Coulomb, C.R. Acad. Sc. Paris, Sér. A 290 (1980), 263-265. MR 81h:73051
- [Fab88]
- Eugene Fabes, Layer potential methods for boundary value problems on Lipschitz domains, Potential theory-surveys and problems (Prague, 1987), Lecture Notes in Math., vol. 1344, Springer, Berlin, 1988, pp. 55-80. MR 89m:31001
- [Jar83]
- Ji\v{r}í Jaru\v{s}ek, Contact problems with bounded friction, coercive case, Czech. Math. J. 108 (1983), 237-261. MR 84h:73045
- [NJH80]
- Jind\v{r}ich Ne\v{c}as, Ji\v{r}í Jaru\v{s}ek, and Jaroslav Haslinger, On the solution of the variational inequality to the Signorini problem with small friction, Bolletino U.M.I., series 5 17B (1980), 796-811. MR 82a:49015
- [Ste70]
- E.M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, Princeton NJ, 1970. MR 44:7280
- [Tor86]
- A. Torchinsky, Real variable methods in harmonic analysis, Academic Press, 1986. MR 88e:42001
- [Ver84]
- G.C. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace's equation on Lipschitz domains, J. Funct. Anal. 59 (1984), 572-611. MR 86e:35038
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Additional Information:
Russell
M.
Brown
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email:
rbrown@ms.uky.edu
Zhongwei
Shen
Affiliation:
Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027
Email:
shenz@ms.uky.edu
Peter
Shi
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309-4401
Email:
pshi@oakland.edu
DOI:
10.1090/S0002-9947-98-02205-3
PII:
S 0002-9947(98)02205-3
Keywords:
Contact problems,
Lamé system,
regularity of solutions,
variational inequality
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 of article:
Copyright
1998,
American Mathematical Society
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