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arXiv · 1306.0565

A gradient estimate for harmonic functions sharing the same zeros

Dan Mangoubi
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Abstract

Let u, v be two harmonic functions in the disk of radius two which have exactly the same set Z of zeros. We observe that the gradient of \log |u/v| is bounded in the unit disk by a constant which depends on Z only. In case Z is empty this goes back to Li-Yau's gradient estimate for positive harmonic functions. The general boundary Harnack principle gives H\"older estimates on \log |u/v|.

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Dan Mangoubi. 2013-06-03. A gradient estimate for harmonic functions sharing the same zeros. https://doi.org/10.3934/era.2014.21.62

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