Gradient estimates of nonlinear equation on complete noncompact metric measure space with compact boundary

2022/09/26 by Cao, Xiangzhi
Mathematics · #53C27 #58E15 #58E20 #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2209.12600

openalex publication_date 2022/09/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, firstly, we study gradient estimates for positive solution of the following equation Δ_ξ(u)-∂_t u- q u =A(u),t∈ (-∞,∞) on metric measure space (M,g,e^-ξd v_g) with boundary , where Δ_ξ=Δ+ ⟨ ∇⋅ , ∇ ξ ⟩ . For this equation, we derive Li-Yau type gradient estimates and Hamilton's type gradient estimates. Secondly, we obtain gradient estimates for positive solution of the following elliptical type equation Δ_ξ(u)- q u =A(u) on complete noncompact metric measure space (M,g,e^-ξd v_g) with boundary.

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