Sharp pointwise estimates for the gradients of solutions to linear parabolic second order equation in the layer

@article{Kresin2019SharpPE,
title={Sharp pointwise estimates for the gradients of solutions to linear parabolic second order equation in the layer},
author={G. Kresin and V. Maz'ya},
journal={arXiv: Analysis of PDEs},
year={2019}
}

We deal with solutions of the Cauchy problem to linear both homogeneous and nonhomogeneous parabolic second order equations with real constant coefficients in the layer ${\mathbb R}^{n+1}_T={\mathbb R}^n\times (0, T)$, where $n\geq 1$ and $T n+2$ and $\alpha \in (0, 1)$. Explicit formulas for the sharp coefficients in pointwise estimates for the length of the gradient to solutions to these problems are obtained.