An existence result on noncoercive hemivariational inequalities (Q1130245)

The authors study the existence of solutions to a noncoercive hemivariational inequality on a convex set \(K\) in a real Hilbert space \(V\) which is compactly embedded in \(L^2(\Omega)\) for an open bounded subset in an Euclidean space. The lack of coerciveness for the bilinear form entering the hemivariational inequality is compensated by a strong use of the geometry of the set \(K\) concentrated in its recession cone. The main result provides the existence of a solution by a constructive approximation process combined with a regularization technique. As a particular case one obtains an existence result due to P. D. Panagiotopoulos in the case where \(K= V\). A careful analysis of the relationship with other related results is given.