Gradient estimates for Leibenson's equation on Riemannian manifolds

2025/06/08 by Sürig, Philipp
#35B05 #35K55 #53C21 #58J35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.07221

Abstract

We consider on Riemannian manifolds solutions of the Leibenson equation ∂ _tu=Δ_pu^q. This equation is also known as doubly nonlinear evolution equation. We prove gradient estimates for positive solutions u under the condition that the Ricci curvature on M is bounded from below by a non-positive constant. We distinguish between the case q(p-1)>1 (slow diffusion case) and the case q(p-1)<1 (fast diffusion case).

Citations

• Global existence for a Leibenson type equation with reaction on Riemannian manifolds
• Gradient estimates for the porous medium equations on Riemannian manifolds
• Local Gradient Estimate for p-harmonic functions on Riemannian Manifolds
• Local gradient estimates of p-harmonic functions, 1/H-flow, and an entropy formula

Related

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• Gradient estimates for positive weak solution to Δ_pu+au^σ=0 on Riemannian manifolds