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

preprint2016arXivOpen access

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

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A Remark on Global W1,pW^{1,p}W1,p Bounds for Harmonic Functions with Lipschitz Boundary Values

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