Convergence of Minima and of Minimizers

In this chapter we shall prove that, under some equi-coerciveness assumptions, the Γ-convergence of a sequence (F h ) to a function F implies the convergence of the minimum values of F h to the minimum value of F. Moreover, under the additional hypothes is that F h and F have a unique minimum point, we shall prove that the sequence of the minimizers of F h converges to the minimizer of F.