# Some quantitative Sobolev estimates for planar infinity harmonic functions

## Speaker:

## Institution:

## Time:

## Host:

## Location:

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