Gradient estimates for the porous medium type equations and fast diffusion type equations on complete noncompact metric measure space with compact boundary

2022/10/01 by Cao, Xiangzhi
#53C27 #58E15 #58E20 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.00224

Abstract

In the paper, we derive Li-Yau gradient estimates and Souplet Zhang type estimates of the following equation \beginsplit u_t= Δ_ξp+λu+A(u) , \endsplit on complete noncompact metric measure space (M, g,e^-ξdv_g) with compact boundary. We will also give the local gradient estimates of the equation Δ_ξ(u^p)+λu+A(u)=0, on complete noncompact manifold with compact boundary.

Related

• Gradient estimates of nonlinear equation on complete noncompact metric measure space with compact boundary
• Local estimates for positive solutions of porous medium equations
• Gradient estimates for some evolution equations on complete smooth\n metric measure spaces
• Gradient estimates for the porous medium equations on Riemannian manifolds
• Gradient estimates for u_t=ΔF(u) on manifolds and some Liouville-type theorems