Multivalued superposition operators
Given a bounded domain \(\Omega\) in \(\mathbb{R}^ N\), the authors study the multivalued superposition operator \(N_ F\) generated by a multivalued function \(F: \Omega\times\mathbb{R}\to 2^ \mathbb{R}\). They give continuity and boundedness conditions for \(N_ F\) in the space \(S\) of measurable functions, between two ideal function spaces, and in the space \(C\) of continuous functions. Moreover, they compare the closure \(\overline F\) and the convexification \(F^ \square\) of the function \(F\) with the closure \(\overline N_ F\) and the convexification \(N^ \square_ F\) of the corresponding operator \(N_ F\).
scientific article; zbMATH DE number 60491
scientific article