Some quantitative Sobolev estimates for planar infinity harmonic functions

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Speaker: 
Yi Zhang
Institution: 
Mathematical Institute of the University of Bonn
Time: 
Tue, 01/16/2018 - 3:00pm
Host: 
Yifeng Yu
Location: 
RH306

Given a planar infinity harmonic function u, for each
$\alpha>0$ we show a quantitative $W^{1,\,2}_{\loc}$-estimate of
$|Du|^{\alpha}$, which is sharp when $\alpha\to 0$.  As a consequence we
obtain an $L^p$-Liouville property for infinity harmonic functions in
the whole plane