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Explicit constants in Harnack inequalities and regularity estimates, with an application to the fast diffusion equation

Abstract : This paper is devoted to the computation of various explicit constants in functional inequalities and regularity estimates for solutions of parabolic equations, which are not available from the literature. We provide new expressions and simplified proofs of the Harnack inequality and the corresponding Hölder continuity of the solution of a linear parabolic equation. We apply these results to the computation of a constructive estimate of a threshold time for the uniform convergence in relative error of the solution of the fast diffusion equation.
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https://hal.archives-ouvertes.fr/hal-02887013
Contributor : Jean Dolbeault <>
Submitted on : Friday, July 3, 2020 - 3:51:51 PM
Last modification on : Monday, August 3, 2020 - 3:36:23 AM

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  • HAL Id : hal-02887013, version 1
  • ARXIV : 2007.03419

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Matteo Bonforte, Jean Dolbeault, Bruno Nazaret, Nikita Simonov. Explicit constants in Harnack inequalities and regularity estimates, with an application to the fast diffusion equation. 2020. ⟨hal-02887013⟩

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