A sufficient condition for the lower semicontinuity of nonlocal supremal functionals in the vectorial case

Abstract

We present a sufficient condition ensuring lower semicontinuity for nonlocal supremal functionals of the type "Equation missing"where $$\Omega $$ Ω is a bounded open subset of $${\mathbb {R}}^N$$ R N and $$W:\Omega \,{\times }\, \Omega \,{\times }\, {\mathbb {R}}^{d \times N}{\times }\, {\mathbb {R}}^{d \times N} \rightarrow {\mathbb {R}}.$$ W : Ω × Ω × R d × N × R d × N → R .