The sharp affine $L^2$ Sobolev trace inequality and variants
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2015
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| _version_ | 1866929756373516288 |
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| author | De Nápoli, Pablo Luis Haddad, Julián Jiménez, Carlos Hugo Montenegro, Marcos |
| author_facet | De Nápoli, Pablo Luis Haddad, Julián Jiménez, Carlos Hugo Montenegro, Marcos |
| contents | We establish a sharp affine $L^p$ Sobolev trace inequality by using the $L_p$ Busemann-Petty centroid inequality. For $p = 2$, our affine version is stronger than the famous sharp $L^2$ Sobolev trace inequality proved independently by Escobar and Beckner. Our approach allows also to characterize all cases of equality in this case. For this new inequality, no Euclidean geometric structure is needed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1512_04621 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | The sharp affine $L^2$ Sobolev trace inequality and variants De Nápoli, Pablo Luis Haddad, Julián Jiménez, Carlos Hugo Montenegro, Marcos Functional Analysis Analysis of PDEs Primary 46E35, Secondary 46E39, 51M16 We establish a sharp affine $L^p$ Sobolev trace inequality by using the $L_p$ Busemann-Petty centroid inequality. For $p = 2$, our affine version is stronger than the famous sharp $L^2$ Sobolev trace inequality proved independently by Escobar and Beckner. Our approach allows also to characterize all cases of equality in this case. For this new inequality, no Euclidean geometric structure is needed. |
| title | The sharp affine $L^2$ Sobolev trace inequality and variants |
| topic | Functional Analysis Analysis of PDEs Primary 46E35, Secondary 46E39, 51M16 |
| url | https://arxiv.org/abs/1512.04621 |