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 $L_{\loc}^{2+\varepsilon}$, $\varepsilon>0$. We establish Hölder continuity of the bounded soutions, sharp two-sided Gaussian bound on the heat kernel, Harnack inequality.
Citation
Damir Kinzebulatov. Yuliy A. Semënov. "Kolmogorov operator with the vector field in Nash class." Tohoku Math. J. (2) 74 (4) 569 - 596, 2022. https://doi.org/10.2748/tmj.20210825
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