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arXiv:2105.15016 [math.AP]AbstractReferencesReviewsResources

Weak Harnack inequality for a mixed local and nonlocal parabolic equation

Prashanta Garain, Juha Kinnunen

Published 2021-05-31Version 1

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 H\"older inequality and a logarithmic estimate for weak supersolutions.

Comments: 27 pages
Categories: math.AP
Subjects: 35R11, 35K05, 35B65, 47G20, 35D30
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