Classification results for bounded positive solutions to the critical $p$-Laplace equation
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918303397576704 |
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| author | Ciraolo, Giulio Gatti, Michele |
| author_facet | Ciraolo, Giulio Gatti, Michele |
| contents | By providing optimal or nearly optimal integral estimates, we show that every positive, bounded or moderately growing, local weak solution to the critical $p$-Laplace equation in $\mathbb{R}^n$, with $n\geq 3$, and whose infimum over a ball behaves properly must be a bubble. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23243 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Classification results for bounded positive solutions to the critical $p$-Laplace equation Ciraolo, Giulio Gatti, Michele Analysis of PDEs 35B33, 35J92 (Primary) 35B09 (Secondary) By providing optimal or nearly optimal integral estimates, we show that every positive, bounded or moderately growing, local weak solution to the critical $p$-Laplace equation in $\mathbb{R}^n$, with $n\geq 3$, and whose infimum over a ball behaves properly must be a bubble. |
| title | Classification results for bounded positive solutions to the critical $p$-Laplace equation |
| topic | Analysis of PDEs 35B33, 35J92 (Primary) 35B09 (Secondary) |
| url | https://arxiv.org/abs/2510.23243 |