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arXiv · 1601.00190

A Remark on Global $W^{1,p}$ Bounds for Harmonic Functions with Lipschitz Boundary Values

Nikos Katzourakis
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Abstract

In this note we show that gradient of Harmonic functions on a smooth domain with Lipschitz boundary values is pointwise bounded by a universal function which is in $L^p$ for all finite $p\geq 1$.

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Nikos Katzourakis. 2016-07-01. A Remark on Global $W^{1,p}$ Bounds for Harmonic Functions with Lipschitz Boundary Values. https://arxiv.org/abs/1601.00190

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