Some results on a class of degenerate parabolic equations not in divergence form

2005 ◽  
Vol 60 (5) ◽  
pp. 863-886 ◽  
Author(s):  
Wenshu Zhou ◽  
Zhuoqun Wu
Keyword(s):  
Parabolic Equations ◽  
Divergence Form ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic

scholarly journals Hölder gradient estimates for a class of singular or degenerate parabolic equations

2017 ◽  
Vol 8 (1) ◽  
pp. 845-867 ◽  
Author(s):  
Cyril Imbert ◽  
Tianling Jin ◽  
Luis Silvestre
Keyword(s):  
Parabolic Equation ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equation ◽  
Divergence Form ◽  
Gradient Estimates ◽  
Degenerate Parabolic Equations ◽  
Spatial Gradients ◽  
Degenerate Parabolic ◽  
Laplacian Equations ◽  
Hölder Estimates

Abstract We prove interior Hölder estimates for the spatial gradients of the viscosity solutions to the singular or degenerate parabolic equation u_{t}=\lvert\nabla u\rvert^{\kappa}\operatorname{div}(\lvert\nabla u\rvert^{p-% 2}\nabla u), where {p\in(1,\infty)} and {\kappa\in(1-p,\infty)} . This includes the from {L^{\infty}} to {C^{1,\alpha}} regularity for parabolic p-Laplacian equations in both divergence form with {\kappa=0} , and non-divergence form with {\kappa=2-p} .

Sign in / Sign up

Export Citation Format

Share Document