TITLE

A GRADIENT ESTIMATE FOR HARMONIC FUNCTIONS SHARING THE SAME ZEROS

AUTHOR(S)
MANGOUBI, DAN
PUB. DATE
January 2014
SOURCE
Electronic Research Announcements in Mathematical Sciences;2014, Vol. 21, p62
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
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∣.
ACCESSION #
96805929

 

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