Rigidity of solutions to singular/degenerate semilinear critical equations
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912438509633536 |
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| author | Catino, Giovanni Monticelli, Dario Daniele Roncoroni, Alberto |
| author_facet | Catino, Giovanni Monticelli, Dario Daniele Roncoroni, Alberto |
| contents | This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in $\mathbb{R}^d$, with $d\geq 2$. We prove several rigidity results for positive solutions, in particular we classify solutions with possibily infinite energy when the intrinsic dimension $n$ satisfies $2<n<4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15611 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rigidity of solutions to singular/degenerate semilinear critical equations Catino, Giovanni Monticelli, Dario Daniele Roncoroni, Alberto Analysis of PDEs This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in $\mathbb{R}^d$, with $d\geq 2$. We prove several rigidity results for positive solutions, in particular we classify solutions with possibily infinite energy when the intrinsic dimension $n$ satisfies $2<n<4$. |
| title | Rigidity of solutions to singular/degenerate semilinear critical equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.15611 |