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Extra regularity for parabolic equations with drift terms. (English) Zbl 1063.35045
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.

35B65 Smoothness and regularity of solutions to PDEs
35K10 Second-order parabolic equations
35A08 Fundamental solutions to PDEs
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