Composition operators in Orlicz-Sobolev spaces

TL;DR

This paper investigates the continuity of Nemytskii operators in Orlicz-Sobolev spaces, extending classical Sobolev results and including anisotropic cases, with new findings even for standard anisotropic Sobolev spaces.

Contribution

It extends and improves classical Sobolev space results to Orlicz-Sobolev spaces, including anisotropic cases, providing new insights even for standard anisotropic Sobolev spaces.

Findings

Established continuity results for Nemytskii operators in Orlicz-Sobolev spaces.

Extended classical Sobolev results to more general Orlicz-Sobolev settings.

Included anisotropic Orlicz-Sobolev spaces, providing new results for these spaces.

Abstract

The continuity of the Nemytskii operator between Orlicz-Sobolev spaces is investigated. Natural Orlicz-Sobolev versions of classical results for standard Sobolev are established. The results presented not only extend the latter, but also improve them in borderline situations. Anisotropic Orlicz-Sobolev spaces are included in our analysis. The results offered for this class of spaces are new even for customary anisotropic Sobolev spaces.