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Transactions of the American Mathematical Society

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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
MathSciNet review: 1475678
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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.

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Additional Information

Russell M. Brown
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027

Zhongwei Shen
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027

Peter Shi
Affiliation: Department of Mathematical Sciences, Oakland University, Rochester, Michigan 48309-4401

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.
Article copyright: © Copyright 1998 American Mathematical Society

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