Zero-extension convergence and Sobolev spaces on changing domains
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915025893982208 |
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| author | Evseev, Nikita Kampschulte, Malte Menovschikov, Alexander |
| author_facet | Evseev, Nikita Kampschulte, Malte Menovschikov, Alexander |
| contents | We extend the definition of weak and strong convergence to sequences of Sobolev-functions whose underlying domains themselves are converging. In contrast to previous works, we do so without ever assuming any sort of reference configuration. We then develop the respective theory and counterparts to classical compactness theorems from the fixed domain case. Finally, we illustrate the usefulness of these definitions with some examples from applications and compare them to other approaches. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_10827 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Zero-extension convergence and Sobolev spaces on changing domains Evseev, Nikita Kampschulte, Malte Menovschikov, Alexander Analysis of PDEs Functional Analysis We extend the definition of weak and strong convergence to sequences of Sobolev-functions whose underlying domains themselves are converging. In contrast to previous works, we do so without ever assuming any sort of reference configuration. We then develop the respective theory and counterparts to classical compactness theorems from the fixed domain case. Finally, we illustrate the usefulness of these definitions with some examples from applications and compare them to other approaches. |
| title | Zero-extension convergence and Sobolev spaces on changing domains |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2411.10827 |