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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.09366 |
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Table of 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.