Harnack inequality for nonlinear parabolic equations under integral Ricci curvature bounds

2022/06/23 by Azami, Shahroud
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.13229

Abstract

Let (Mⁿ,g) be a complete Riemannian manifold. In this paper, we establish a space-time gradient estimates for positive solutions of nonlinear parabolic equations ∂_tu(x,t)=Δu(x,t)+a u(x,t)(log u(x,t))^b + q(x,t)A(u(x,t)), on geodesic balls B(O,r) in M with 0(n)/(2) when integral Ricci curvature k(p,1) is small enough. By integrating the gradient estimates, we find the corresponding Harnack inequalities.

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