Regularity of solutions to a contact problem

Authors:
Russell M. Brown, Zhongwei Shen and Peter Shi

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

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Abstract | References | Similar Articles | Additional Information

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.

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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:
https://doi.org/10.1090/S0002-9947-98-02205-3

Keywords:
Contact problems,
LamÃ© 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.

Article copyright:
© Copyright 1998
American Mathematical Society