Revisited convexity notions for $$L^\infty $$ variational problems

Abstract

AbstractWe 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 $$L^p$$ L p -approximation, as $$p \rightarrow +\infty $$ 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 $$L^\infty $$ L ∞ context.