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arXiv · 2404.09702

Higher-order Sobolev embeddings into spaces of Campanato and Morrey type

Paola Cavaliere·Andrea Cianchi·Luboš Pick·Lenka Slavíková
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Abstract

Necessary and sufficient conditions are offered for Sobolev type spaces built on rearrangement-invariant spaces to be continuously embedded into (generalized) Campanato and Morrey spaces on open subsets of the $n$-dimensional Euclidean space. As a consequence, the optimal target and domain spaces in the relevant embeddings are identified. Our general criteria are implemented to derive sharp embeddings in the class of Orlicz-Sobolev spaces.

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Paola Cavaliere, Andrea Cianchi, Luboš Pick, Lenka Slavíková. 2024-04-15. Higher-order Sobolev embeddings into spaces of Campanato and Morrey type. https://arxiv.org/abs/2404.09702

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