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Composition operators in Orlicz–Sobolev spaces
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The continuity of the Nemytskii operator between Orlicz–Sobolev spaces is investigated. Natural Orlicz–Sobolev versions of classical results for standard Sobolev spaces are established. The results presented not only extend the latter, but also improve them in borderline situations. Anisotropic Orlicz–Sobolev spaces are also included. The results offered for this class of spaces are new even for customary anisotropic Sobolev spaces.
World Scientific Pub Co Pte Ltd
Title: Composition operators in Orlicz–Sobolev spaces
Description:
The continuity of the Nemytskii operator between Orlicz–Sobolev spaces is investigated.
Natural Orlicz–Sobolev versions of classical results for standard Sobolev spaces are established.
The results presented not only extend the latter, but also improve them in borderline situations.
Anisotropic Orlicz–Sobolev spaces are also included.
The results offered for this class of spaces are new even for customary anisotropic Sobolev spaces.
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