Weak Harnack inequality for a mixed local and nonlocal parabolic equation
JOURNAL OF DIFFERENTIAL EQUATIONS(2023)
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 Holder inequality and a logarithmic estimate for weak supersolutions.(c) 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).
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Key words
Mixed local and nonlocal Laplace operator,Energy estimates,Moser iteration,Reverse H?lder inequality,Weak Harnack inequality
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