Revisited convexity notions for L^∞ variational problems

We address a detailed study of the convexity notions that arise in the study of weak* lower semicontinuity of supremal functionals, as well as those arising by the Lᵖ L p -approximation, as p → +∞ p → + ∞ of such functionals. Our quest is motivated by the knowledge we have on the analogous integral functionals and aims at establishing a solid groundwork underlying further research in the L^∞ L ∞ context.