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MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 281-292 (2001)
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# On the minimum of the work of interaction forces between a pseudoplate and a rigid obstacle

## Igor Bock, Jan Lovisek

* Igor Bock*, Department of Mathematics, Faculty of Electr. Engineering and Inform. Tech., Slovak University of Technology, Ilkovicova 3, 812 19 Bratislava, Slovakia, e-mail: ` bock@kmat.elf.stuba.sk`; * Jan Lovisek*, Department of Mechanics, Faculty of Civil Engineering, Slovak University of Technology, Radlinského 11, 813 68 Bratislava, Slovakia, e-mail: ` lovisek@svf.stuba.sk`

**Abstract:**
An optimization problem for the unilateral contact between a pseudoplate and a rigid obstacle is considered. The variable thickness of the pseudoplate plays the role of a control variable. The cost functional is a regular functional only in the smooth case. The existence of an optimal thickness is verified. The penalized optimal control problem is considered in the general case.

**Keywords:** elliptic variational inequality, pseudoplate, thickness, optimal control, penalization

**Classification (MSC2000):** 49J20, 35J85

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