On a supercritical Hardy-Sobolev type inequality with logarithmic term and related extremal problem
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910939588067328 |
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| author | de Oliveira, José Francisco Silva, Jeferson |
| author_facet | de Oliveira, José Francisco Silva, Jeferson |
| contents | Our main goal is to investigate supercritical Hardy-Sobolev type inequalities with a logarithmic term and their corresponding variational problem. We prove the existence of extremal functions for the associated variational problem, despite the loss of compactness. As an application, we show the existence of weak solution to a general class of related elliptic partial differential equations with a logarithmic term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19128 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a supercritical Hardy-Sobolev type inequality with logarithmic term and related extremal problem de Oliveira, José Francisco Silva, Jeferson Analysis of PDEs 46E35, 35J35, 35J61, 35B33 Our main goal is to investigate supercritical Hardy-Sobolev type inequalities with a logarithmic term and their corresponding variational problem. We prove the existence of extremal functions for the associated variational problem, despite the loss of compactness. As an application, we show the existence of weak solution to a general class of related elliptic partial differential equations with a logarithmic term. |
| title | On a supercritical Hardy-Sobolev type inequality with logarithmic term and related extremal problem |
| topic | Analysis of PDEs 46E35, 35J35, 35J61, 35B33 |
| url | https://arxiv.org/abs/2406.19128 |