Extra regularity for parabolic equations with drift terms (Q1434138)

A parabolic equation with a drift term \(u_t=\Delta u +b \nabla u\) is considered in \(\mathbb R^n\times (0, \infty), \;b=b(x)\) is \(n\)-dimensional vector-function. The goal of the article is to establish Gaussian bounds for the fundamental solution and Hölder continuity of solutions under the maximal possible singularity of the drift term. For specific drift the results are given for singularities of \(b\) up to the limit order \(c/| x| \), -- in contrast to singular potential terms.