caa a22 4500 606193944 CHVBK 20210128100912.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s00030-015-0337-y doi (NATIONALLICENCE)springer-10.1007/s00030-015-0337-y Prinari Francesca Dip. di Matematica e Informatica, Università di Ferrara, Via Machiavelli 35, 44121, Ferrara, Italy aut On the lower semicontinuity and approximation of $${L^{\infty}}$$ L ∞ -functionals [Elektronische Daten] [Francesca Prinari] In this paper we show that if the supremal functional $$F(V,B)= \mathop{\rm ess sup} \limits_{x \in B} f(x,DV (x))$$ F ( V , B ) = ess sup x ∈ B f ( x , D V ( x ) ) is sequentially weak* lower semicontinuous on $${W^{1,\infty}(B, \mathbb{R}^d)}$$ W 1 , ∞ ( B , R d ) for every open set $${B \subseteq \Omega}$$ B ⊆ Ω (where $${\Omega}$$ Ω is a fixed open set of $${\mathbb{R}^N}$$ R N ), then $${f(x,\cdot)}$$ f ( x , · ) is rank-one level convex for a.e $${x \in \Omega}$$ x ∈ Ω . Next, we provide an example of a weak Morrey quasiconvex function which is not strong Morrey quasiconvex. Finally we discuss the L p -approximation of a supremal functional F via $${\Gamma}$$ Γ -convergence when f is a non-negative and coercive Carathéodory function. Springer Basel, 2015 Supremal functionals nationallicence Lower semicontinuity nationallicence Strong Morrey quasiconvexity nationallicence $${\Gamma}$$ Γ -convergence nationallicence Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1591-1605 1021-9722 22:6<1591 2015 22 30 https://doi.org/10.1007/s00030-015-0337-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00030-015-0337-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Prinari Francesca Dip. di Matematica e Informatica, Università di Ferrara, Via Machiavelli 35, 44121, Ferrara, Italy aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Springer Basel 22/6(2015-12-01), 1591-1605 1021-9722 22:6<1591 2015 22 30