Date: 14 Jun 2012

Stationary Inclusions and Hemivariational Inequalities

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In this chapter we study stationary operator inclusions, i.e., inclusions in which the derivatives of the unknown with respect to the time variable are not involved. We start with a basic existence result for abstract operator inclusions. Then we use it in order to prove the existence of solutions for various operator inclusions of subdifferential type. We also prove that, under additional assumptions, the solution of the corresponding inclusions is unique. Finally, we specialize our existence and uniqueness results in the study of stationary hemivariational inequalities. The theorems presented in this chapter will be applied in the study of static frictional contact problems in Chap. 7.