Biharmonic nonlinear vector field equations in $\mathbb{R}^4$
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911394734014464 |
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| author | Arkoudis, Ioannis Smyrnelis, Panayotis |
| author_facet | Arkoudis, Ioannis Smyrnelis, Panayotis |
| contents | Following the approach of Brezis and Lieb, we prove the existence of a ground state solution for the biharmonic nonlinear vector field equations in the limiting case of space dimension $4$. Our results complete those obtained by Mederski and Siemianowski for dimensions $d\geq 5$. We also extend the biharmonic logarithmic Sobolev inequality to dimension $4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Biharmonic nonlinear vector field equations in $\mathbb{R}^4$ Arkoudis, Ioannis Smyrnelis, Panayotis Analysis of PDEs 35J91, 35J20, 35B38, 35Qxx Following the approach of Brezis and Lieb, we prove the existence of a ground state solution for the biharmonic nonlinear vector field equations in the limiting case of space dimension $4$. Our results complete those obtained by Mederski and Siemianowski for dimensions $d\geq 5$. We also extend the biharmonic logarithmic Sobolev inequality to dimension $4$. |
| title | Biharmonic nonlinear vector field equations in $\mathbb{R}^4$ |
| topic | Analysis of PDEs 35J91, 35J20, 35B38, 35Qxx |
| url | https://arxiv.org/abs/2508.14640 |