论文标题
在Riemannian歧管上的加权$ p $ -laplacian方程的梯度估计，具有sobolev不平等和整体ricci界限
Gradient estimates for weighted $p$-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds
论文作者
论文摘要
在本文中，我们考虑非线性通用$ p $ -laplacian方程$δ_{p，f} u+f（u）= 0 $对于平滑度量度量空间的平滑函数$ f $。假设Sobolev不平等在$ M $上是正确的，并且整体RICCI曲率很小，我们首先证明了方程式的局部梯度估计。然后，作为其应用，我们证明了在RICCI曲率下限的歧管上证明了几种liouville型结果。我们还得出了新的局部梯度估计，只要整数RICCI曲率足够小。
In this paper, we consider the non-linear general $p$-Laplacian equation $Δ_{p,f}u+F(u)=0$ for a smooth function $F$ on smooth metric measure spaces. Assume that a Sobolev inequality holds true on $M$ and an integral Ricci curvature is small, we first prove a local gradient estimate for the equation. Then, as its applications, we prove several Liouville type results on manifolds with lower bounds of Ricci curvature. We also derive new local gradient estimates provided that the integral Ricci curvature is small enough.
