Gradient estimates for weighted p-Laplacian equations on Riemannian manifolds with a Sobolev inequality and integral Ricci bounds

2020/07/29 by Lê Văn Đại, Van Dai, Le, Nguyen Thac Dung +5 · 1 citation
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Primary 58J05 #Secondary 58J35

paper · pdf · doi:10.48550/arxiv.2007.14669

openalex publication_date 2020/07/29 · openalex created_date 2022/09/12 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the non-linear general p-Laplacian equation Δ_p,fu+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.

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• Gradient estimates for (p,V)-harmonic functions on Riemannian manifolds

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