Maximum Principles for Optimal Controls for Elliptic Variational Inequalities of the Second Kind

A maximum principle is obtained for optimal controls for someelliptic variational inequalities of the second kind by usingthe penalty method, Ekelans's variational principle, and lowersemicontinuity of some set-valued mappings. It has been shownthat this principle leads to some known optimality conditionsin many cases. It also yields new optimality conditions. Insome cases, it leads to an analogy of pontryagin's principle. Permanent address: Mathematics Department, Centre South Universityof Technology, China.