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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

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: 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, 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