Kolmogorov operator with the vector field in Nash class (Q2679745)

In this interesting paper, the authors 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 \(L^p\), with \(p>n\) (with \(n\) the dimension of the space) as well as some vector fields that are not even in \( L^{2 + \varepsilon}_{\mathrm{loc}}\) with \(\varepsilon\) any positive constant. The authors, using classical regularity approaches, establish Hölder continuity of the bounded solutions, sharp two-sided Gaussian bound on the heat kernel and Harnack inequality.