Abstract
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 , where
and
. The homogeneous equation is considered with initial data in
,
. For the nonhomogeneous equation we suppose that initial function is equal to zero and the function in the right-hand side belongs to
, p>n + 2 and
. 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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Acknowledgements
The publication has been prepared with the support of the ‘RUDN University Program 5–100’.
Disclosure statement
No potential conflict of interest was reported by the authors.