Sharp estimates for the gradient of solutions to the heat equation

G. Kresin; V. Maz'ya

doi:10.1090/SPMJ/1610

Sharp estimates for the gradient of solutions to the heat equation

G. Kresin, V. Maz'ya

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	495-507
Number of pages	13
Journal	St. Petersburg Mathematical Journal
Volume	31
Issue number	3
DOIs	https://doi.org/10.1090/SPMJ/1610
State	Published - 2020

Keywords

First and second boundary value problems
Heat equation
Sharp pointwise estimates for the gradient

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10.1090/SPMJ/1610

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title = "Sharp estimates for the gradient of solutions to the heat equation",

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 Lp. 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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AB - 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 Lp. 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.

KW - First and second boundary value problems

KW - Heat equation

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Sharp estimates for the gradient of solutions to the heat equation

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Keywords

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