In the paper "A handbook of Γ-convergence" I've read the following:
"This is the fundamental theorem of Γ-convergence, that is summarized by the implication Γ-convergence + equicoerciveness $\implies$ convergence of minimum problems".
My question is - if we want to construct a sequence of the functionals which has (the limits are exist) a $\Gamma$-limit and a pointwise limit but they're not equal, then can we take a sequence which is not equicoercive?