NONLINEAR EIGENVALUE PROBLEMS IN ELLIPTIC VARIATIONAL INEQUALITIES: SOME RESULTS FOR THE MAXIMAL BRANCH.

We study the maximal branch of solutions for a bifurcation phenonemon in variational inequalities. We give optimal results in L** infinity norm for the approximation by finite element method and sharp estimates for the localization of the continuous and discrete free boundary as the bifurcation parameter goes to infinity. We also obtain Lipschitz regularity results for the maximal branch. We establish in some cases a stability condition which has appeared of great importance in the description of the bifurcation phenomenon and in the numerical analysis study.