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arXiv · 2405.04482

Harnack inequality for parabolic equations in double-divergence form with singular lower order coefficients

Istvan Gyöngy·Seick Kim
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Abstract

This paper investigates the Harnack inequality for nonnegative solutions to second-order parabolic equations in double divergence form. We impose conditions where the principal coefficients satisfy the Dini mean oscillation condition in $x$, while the drift and zeroth-order coefficients belong to specific Morrey classes. Our analysis contributes to advancing the theoretical foundations of parabolic equations in double divergence form, including Fokker-Planck-Kolmogorov equations for probability densities.

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Istvan Gyöngy, Seick Kim. 2024-05-07. Harnack inequality for parabolic equations in double-divergence form with singular lower order coefficients. https://doi.org/10.1016/j.jde.2024.08.070

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