Weak Harnack inequality for a mixed local and nonlocal parabolic equation
Prashanta Garain, Juha Kinnunen
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.
Topics & Concepts
Harnack's inequalityMathematicsLemma (botany)Harnack's principleLogarithmMathematical analysisParabolic partial differential equationInequalityApplied mathematicsPartial differential equationEcologyPoaceaeBiologyNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringAdvanced Mathematical Physics Problems