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An $L^p$-comparison, $p\in (1,\infty)$, on the finite differences of a discrete harmonic function at the boundary of a discrete box by Nguyen, Tuan Anh is a scholarly article available to read on EtoBox.

What is An $L^p$-comparison, $p\in (1,\infty)$, on the finite differences of a discrete harmonic function at the boundary of a discrete box about?

It is well-known that for a harmonic function $u$ defined on the unit ball of the $d$-dimensional Euclidean space, $d\geq 2$, the tangential and normal component of the gradient $\nabla u$ on the sphere are comparable by means of the $L^p$-norms, $p\in(1,\infty)$, up to multiplicative constants that depend only on $d,p$. This paper formulates and proves a discrete analogue of this result for discrete harmonic functions defined on a discrete box on the $d$-dimensional lattice with multiplicative constants that do not depend on the size of the box.

Author

Nguyen, Tuan Anh

Published

2019

Language

EN