New analytical and geometrical aspects on Trudinger-Moser type inequality in 2D
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910433912291328 |
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| author | Borgia, Natalino Cingolani, Silvia Mancini, Gabriele |
| author_facet | Borgia, Natalino Cingolani, Silvia Mancini, Gabriele |
| contents | The present survey is devoted to results on Trudinger-Moser inequalities in two dimension. We give a brief overview of the history of these celebrated inequalities and, starting from the geometric problem that motivated Moser's original work, we discuss the connection between Onofri's inequality for the unit sphere and sharp inequalities on Euclidean domains. Finally, we present recent results and new insights into nonlocal interaction energy functionals in two dimension, involving logarithmic kernels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02118 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New analytical and geometrical aspects on Trudinger-Moser type inequality in 2D Borgia, Natalino Cingolani, Silvia Mancini, Gabriele Analysis of PDEs 35A23, 35A15, 35J50, 35B38, 35J15, 45K05, 58J90 The present survey is devoted to results on Trudinger-Moser inequalities in two dimension. We give a brief overview of the history of these celebrated inequalities and, starting from the geometric problem that motivated Moser's original work, we discuss the connection between Onofri's inequality for the unit sphere and sharp inequalities on Euclidean domains. Finally, we present recent results and new insights into nonlocal interaction energy functionals in two dimension, involving logarithmic kernels. |
| title | New analytical and geometrical aspects on Trudinger-Moser type inequality in 2D |
| topic | Analysis of PDEs 35A23, 35A15, 35J50, 35B38, 35J15, 45K05, 58J90 |
| url | https://arxiv.org/abs/2405.02118 |