Variational Inequalities and the Signorini Problem for Nonlinear Material

With regard to the general nonlinear model of Section 62.3 we now consider boundary-value problems, for which the elastic body is supported on parts of its boundary. The boundary conditions thereby have the form of inequalities. In functional-analytic terms, this leads to convex variational problems on convex sets. The corresponding Euler equations are variational inequalities. We shall use Theorem 46.A of Part III in order to obtain a general existence and uniqueness theorem. Throughout, the same notation as in the previous chapter will be employed.