Sharp estimates for the gradient of solutions to the heat equation

2018/08/09 by Kresin, Gershon, Maz'ya, Vladimir
#Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35K05 #Secondary 26D20

paper · doi:10.48550/arxiv.1808.03101

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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