Weak Harnack inequality for a mixed local and nonlocal parabolic equation

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2023-07-05
Major/Subject
Mcode
Degree programme
Language
en
Pages
34
373-406
Series
Journal of Differential Equations, Volume 360
Abstract
This article proves a weak Harnack inequality with a tail term for sign changing supersolutions of a mixed local and nonlocal parabolic equation. Our argument is purely analytic. It is based on energy estimates and the Moser iteration technique. Instead of the parabolic John-Nirenberg lemma, we adopt a lemma of Bombieri-Giusti to the mixed local and nonlocal parabolic case. To this end, we prove an appropriate reverse Hölder inequality and a logarithmic estimate for weak supersolutions.
Description
Publisher Copyright: © 2023 The Author(s)
Keywords
Energy estimates, Mixed local and nonlocal Laplace operator, Moser iteration, Reverse Hölder inequality, Weak Harnack inequality
Other note
Citation
Garain, P & Kinnunen, J 2023, ' Weak Harnack inequality for a mixed local and nonlocal parabolic equation ', Journal of Differential Equations, vol. 360, pp. 373-406 . https://doi.org/10.1016/j.jde.2023.02.049