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Updated: Feb 20, 2026

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Estimaciones ponderadas de Aronson-Bénilan y desigualdades de Harnack para ecuaciones de difusión lenta con un

Ali Taheri¹, Vahideh Vahidifar¹

¹School of Mathematical and Physical Sciences, University of Sussex, Falmer, Brighton, United Kingdom.

Nonlinear differential equations and applications : NoDEA

|February 19, 2026

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.

Palabras clave:

Estimaciones de Aronson-Bénilan Desigualdad de Harnack Estimaciones de Li-Yau Difusión no lineal Ecuación de difusión lenta Espacios métricos de medida suaves

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