Weak Harnack inequality for a mixed local and nonlocal parabolic equation

2021/05/31 by Garain, Prashanta, Kinnunen, Juha · 4 citations
#35B65 #35D30 #35K05 #35R11 #47G20 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.15016

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 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.

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• Regularity and existence for a mixed local-nonlocal parabolic equation with variable singularities and measure data
• Regularity for Mixed Local and Nonlocal Degenerate Elliptic Equations in the Heisenberg Group

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