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arXiv · 2012.02843

Kolmogorov operator with the vector field in Nash class

D. Kinzebulatov·Yu. A. Semenov
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Abstract

We consider divergence-form parabolic equation with measurable uniformly elliptic matrix and the vector field in a large class containing, in particular, the vector fields in $L^p$, $p>d$, as well as some vector fields that are not even in $L_{\rm loc}^{2+\varepsilon}$, $\varepsilon>0$. We establish H\"{o}lder continuity of the bounded soutions, sharp two-sided Gaussian bound on the heat kernel, Harnack inequality.

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D. Kinzebulatov, Yu. A. Semenov. 2020-12-04. Kolmogorov operator with the vector field in Nash class. https://arxiv.org/abs/2012.02843

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