ON THE DUAL RECIPROCAL VARIATIONAL APPROACH TO THE SIGNORINI-FICHERA PROBLEM - CONVEX AND NONCONVEX GENERALIZATION

The aim of the present paper is the study of a new variational formulation for the Signorini-Fichera problem. It is the dual reciprocal variational formulation which gives rise to an inequality constrained minimum only with respect to the unknown unilateral displacements. In the present paper the dual reciprocal variational problem is formulated for general unilateral boundary conditions derived from convex or nonconvex superpotentials. We obtain boundary variational or hemivariational inequalities and we study both for the coercive and the most important semicoercive case the existence and uniqueness (if any) of the solution. To this end a new form of Korn's inequality at the boundary is applied.