January 2014
Electronic Research Announcements in Mathematical Sciences;2014, Vol. 21, p62
Academic Journal
Let u,v be two harmonic functions in {∣z∣ < 2} ⊂ C which have exactly the same set Z of zeros. We observe that ∣∇log∣u/v∣∣ is bounded in the unit disk by a constant which depends on Z only. In case Z = ∅ this goes back to Li-Yau's gradient estimate for positive harmonic functions. The general boundary Harnack principle gives only Hölder estimates on log ∣u/v∣.


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