A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866929697222295552 |
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| author | Ponce, Augusto C. Spector, Daniel |
| author_facet | Ponce, Augusto C. Spector, Daniel |
| contents | We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space $W^{k,1}(\mathbb{R}^d)$ as the difference of two non-negative functions in the same space with control of their norms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1807_05221 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$ Ponce, Augusto C. Spector, Daniel Functional Analysis We show how a strong capacitary inequality can be used to give a decomposition of any function in the Sobolev space $W^{k,1}(\mathbb{R}^d)$ as the difference of two non-negative functions in the same space with control of their norms. |
| title | A decomposition by non-negative functions in the Sobolev space $W^{k, 1}$ |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/1807.05221 |