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IMA Journal of Mathematical Control and Information 1991 8(3):211-230; doi:10.1093/imamci/8.3.211
© 1991 by Institute of Mathematics and its Applications
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Maximum Principles for Optimal Controls for Elliptic Variational Inequalities of the Second Kind

LIU WENBINM {dagger} and J. E. RUBIO

School of Mathematics, University of Leeds Leeds LS2 9JT, U.K.

A maximum principle is obtained for optimal controls for some elliptic variational inequalities of the second kind by using the penalty method, Ekelans's variational principle, and lower semicontinuity of some set-valued mappings. It has been shown that this principle leads to some known optimality conditions in many cases. It also yields new optimality conditions. In some cases, it leads to an analogy of pontryagin's principle.

{dagger} Permanent address: Mathematics Department, Centre South University of Technology, China.


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