Γ-convergence and absolute minimizers for supremal functionals
Thierry Champion, Luigi De Pascale, Francesca Prinari · ESAIM Control Optimisation and Calculus of Variations · 2004
In this paper, we prove that the Lp approximants naturally associated to a supremal functional -converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer (i.e. local solution) among these minimizers. We provide two dierent proofs of this fact relying on dierent assumptions and techniques.