Sharp estimates for the gradient of solutions to the heat equation

Gershon Kresin; Vladimir Maz'ya

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arXiv · 1808.03101

Sharp estimates for the gradient of solutions to the heat equation

Gershon Kresin·Vladimir Maz'ya

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Abstract

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.

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Gershon Kresin, Vladimir Maz'ya. 2018-08-09. Sharp estimates for the gradient of solutions to the heat equation. https://arxiv.org/abs/1808.03101

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