Universal gradient estimates for solutions of $Δ_{p,f}u+au^σ\ln u=0$ on complete Riemannian manifolds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918433516421120 |
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| author | Liu, Jingxu Wang, Zhen |
| author_facet | Liu, Jingxu Wang, Zhen |
| contents | In this paper, we consider the weighted $p$-Laplacian equation $$ Δ_{p,f}u+au^σ\ln u=0$$ defined on a complete smooth metric measure space under the conditon that the $m$-Bakry-Émery Ricci curvature has a lower bound, where $a$, $σ$ are two nonzero real constants. By applying the Nash-Moser iteration, we obtain sharp gradient estimates and thereby establish Liouville theorems for the above equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06605 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal gradient estimates for solutions of $Δ_{p,f}u+au^σ\ln u=0$ on complete Riemannian manifolds Liu, Jingxu Wang, Zhen Differential Geometry In this paper, we consider the weighted $p$-Laplacian equation $$ Δ_{p,f}u+au^σ\ln u=0$$ defined on a complete smooth metric measure space under the conditon that the $m$-Bakry-Émery Ricci curvature has a lower bound, where $a$, $σ$ are two nonzero real constants. By applying the Nash-Moser iteration, we obtain sharp gradient estimates and thereby establish Liouville theorems for the above equation. |
| title | Universal gradient estimates for solutions of $Δ_{p,f}u+au^σ\ln u=0$ on complete Riemannian manifolds |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.06605 |