Higher-order Sobolev embeddings into spaces of Campanato and Morrey type
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916206370357248 |
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| author | Cavaliere, Paola Cianchi, Andrea Pick, Luboš Slavíková, Lenka |
| author_facet | Cavaliere, Paola Cianchi, Andrea Pick, Luboš Slavíková, Lenka |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_09702 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Higher-order Sobolev embeddings into spaces of Campanato and Morrey type Cavaliere, Paola Cianchi, Andrea Pick, Luboš Slavíková, Lenka Functional Analysis 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. |
| title | Higher-order Sobolev embeddings into spaces of Campanato and Morrey type |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2404.09702 |