Integral Harnack estimates and the rate of extinction of singular fractional diffusion

Filippo M. Cassanello; Simone Ciani; Antonio Iannizzotto

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arXiv · 2602.07647

Integral Harnack estimates and the rate of extinction of singular fractional diffusion

Filippo M. Cassanello·Simone Ciani·Antonio Iannizzotto

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Abstract

We prove several integral Harnack-type inequalities for local weak solutions of parabolic equations with measurable and bounded coefficients, describing singular s-fractional p-Laplacian diffusion. Then we apply the aforementioned estimates to evaluate the decay rate of the local mass and supremum of the solutions as they approach a possible extinction time. Yet we show consistency of our general decay estimates by studying the extinction phenomenon for weak solutions of the Cauchy-Dirichlet problem, by means of an approximation procedure that carefully avoids the use of an integrable time derivative.

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Filippo M. Cassanello, Simone Ciani, Antonio Iannizzotto. 2026-02-07. Integral Harnack estimates and the rate of extinction of singular fractional diffusion. https://arxiv.org/abs/2602.07647

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