Weighted Aronson-Bénilan estimates and Harnack inequalities for slow diffusion equations with a nonlinear forcing term
Abstract
We formulate and prove new Aronson-Bénilan and Li-Yau type gradient estimates for positive solutions to nonlinear slow diffusion equations. The framework is that of a smooth metric measure space (i.e., a weighted manifold) and the estimates make use of a range of Harnack quantities with suitable time-variable coefficients. The proofs exploit the intricate relation between geometry, nonlinearity and dynamics of the equation and the results extend, unify and improve various earlier estimates on slow diffusion equations. A number of important corollaries and implications, notably, to parabolic Harnack inequalities and global bounds are presented and discussed.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Differential Geometry Research
Publication details
- Journal / source
- Nonlinear Differential Equations and Applications NoDEA
- Volume
- 33
- Issue
- 2
- Pages
- 54–54
- Publication date
- 16 February 2026
- Language
- EN