Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2411.10757 |
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Inhaltsangabe:
- In this paper, we consider the nonlinear elliptic equation $$Δ_fv^τ+λv=0$$ on a complete smooth metric measure space with $m$-Bakry-Émery Ricci curvature bounded from below, where $τ>0$ and $λ$ are constant. We obtain some new local gradient estimates for positive solutions to the equation using the Nash-Moser iteration technique. As applications of these estimates, we obtain a Liouville type theorem and a Harnack inequality, and the global gradient estimates for such solutions. Our results generalize and improve the estimates in Wang (J. Differential Equations 260:567-585, 2016) and Zhao (Arch. Math. (Basel) 114:457-469, 2020).