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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.16167 |
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| _version_ | 1866912440281726976 |
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| author | Di Blasio, Giuseppina Pisante, Giovanni Psaradakis, Georgios |
| author_facet | Di Blasio, Giuseppina Pisante, Giovanni Psaradakis, Georgios |
| contents | We establish a Leray- Trudinger Type inequality in the anisotropic setting induced by a strongly convex Finsler norm F. The result generalizes classical exponential integrability inequalities for Sobolev functions to the framework of anisotropic Sobolev spaces $W^{1,n}_0(Ω)$, where the standard Euclidean norm is replaced by F and associated polar norm $F^o$. Moreover, in the class of anisotropically radial functions, we obtain the optimal constant in the spirit of Moser's sharp inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_16167 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Anisotropic Improved Leray-Trudinger Inequality Di Blasio, Giuseppina Pisante, Giovanni Psaradakis, Georgios Analysis of PDEs We establish a Leray- Trudinger Type inequality in the anisotropic setting induced by a strongly convex Finsler norm F. The result generalizes classical exponential integrability inequalities for Sobolev functions to the framework of anisotropic Sobolev spaces $W^{1,n}_0(Ω)$, where the standard Euclidean norm is replaced by F and associated polar norm $F^o$. Moreover, in the class of anisotropically radial functions, we obtain the optimal constant in the spirit of Moser's sharp inequality. |
| title | Anisotropic Improved Leray-Trudinger Inequality |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.16167 |