Work

Weighted Aronson-Bénilan estimates and Harnack inequalities for slow diffusion equations with a nonlinear forcing term

Year: 2026

Type: article

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.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-026-01190-7

Authors: Ali Taheri, Vahideh Vahidifar

Institution: University of Sussex

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Engineering and Physical Sciences Research Council