Optimal estimates for the gradient of harmonic functions in the multidimensional half-space

Details Optimal estimates for the gradient of harmonic functions in the multidimensional half-space Optimal estimates for the gradient of harmonic functions in the multidimensional half-space

2009-09-10

arxiv.org/abs/0909.1932v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

A representation of the sharp constant in a pointwise estimate of the
gradient of a harmonic function in a multidimensional half-space is obtained
under the assumption that function's boundary values belong to $L^p$. This
representation is concretized for the cases $p=1, 2,$ and $\infty$.

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