科研之友
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摘要
Let u, v be two harmonic functions in {vertical bar z vertical bar < 2} C C which have exactly the same set Z of zeros. We observe that broken vertical bar del logl vertical bar u/v vertical bar broken vertical bar is bounded in the unit disk by a constant which depends on Z only. In case Z = 0 this goes back to Li-Yau's gradient estimate for positive harmonic functions. The general boundary Harnack principle gives only Holder estimates on logl vertical bar u/v vertical bar.
- 出版日期2014
