Quality of non-compactness for Sobolev Embedding with one point non-compactness
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866909315608084480 |
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| author | Chuah, Chian Yeong Lang, Jan |
| author_facet | Chuah, Chian Yeong Lang, Jan |
| contents | This paper investigates instances of Sobolev embeddings characterized by local compactness at every point within their domain, except for a single point. We obtain the sharp conditions that distinguish compactness from non-compactness and observe that in the context of Sobolev embeddings, non-compactness occurring at only one point within the domain could give rise to an infinite-dimensional subspace where the embedding is invertible (i.e., not strictly singular). Furthermore, we establish lower bounds for the Bernstein numbers, entropy numbers, and the measure of non-compactness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09366 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Quality of non-compactness for Sobolev Embedding with one point non-compactness Chuah, Chian Yeong Lang, Jan Functional Analysis Analysis of PDEs This paper investigates instances of Sobolev embeddings characterized by local compactness at every point within their domain, except for a single point. We obtain the sharp conditions that distinguish compactness from non-compactness and observe that in the context of Sobolev embeddings, non-compactness occurring at only one point within the domain could give rise to an infinite-dimensional subspace where the embedding is invertible (i.e., not strictly singular). Furthermore, we establish lower bounds for the Bernstein numbers, entropy numbers, and the measure of non-compactness. |
| title | Quality of non-compactness for Sobolev Embedding with one point non-compactness |
| topic | Functional Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2309.09366 |