Geodesic
Sharp estimates for the gradient of solutions to the heat equation
Algebra i analiz, Tome 31 (2019) no. 3, pp. 136-153 Cet article a éte moissonné depuis la source Math-Net.Ru

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Various sharp pointwise estimates for the gradient of solutions to the heat equation are obtained. The Dirichlet and Neumann conditions are prescribed on the boundary of a half-space. All data belong to the Lebesgue space $ L^p$. Derivation of the coefficients is based on solving certain optimization problems with respect to a vector parameter inside of an integral over the unit sphere.
Keywords: heat equation, sharp pointwise estimates for the gradient, first and second boundary value problems. 
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G. Kresin; V. Maz'ya. Sharp estimates for the gradient of solutions to the heat equation. Algebra i analiz, Tome 31 (2019) no. 3, pp. 136-153. http://geodesic.mathdoc.fr/item/AA_2019_31_3_a6/

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