Existence of extremal functions in higher-order affine Sobolev inequalities
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917376933494784 |
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| author | Bullion-Gauthier, Tristan |
| author_facet | Bullion-Gauthier, Tristan |
| contents | In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces of arbitrary regularity, might be of independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00640 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of extremal functions in higher-order affine Sobolev inequalities Bullion-Gauthier, Tristan Functional Analysis In this article, we prove the existence of extremal functions in higher-order affine Sobolev inequalities. Proofs rely on concentration-compactness methods in spaces of integer or fractional regularity. The tools we use, available in spaces of arbitrary regularity, might be of independent interest. |
| title | Existence of extremal functions in higher-order affine Sobolev inequalities |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2604.00640 |