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}
}
  • G. Kresin, V. Maz'ya
  • Published 2019
  • Mathematics, Physics
  • arXiv: Analysis of PDEs
  • 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. 
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