How to play with the three spheres theorem.

Monday, October 16, 2017 -
3:30pm to 4:30pm
Please note the different time.Let u be a solution of second order elliptic differential equation Lu = 0. Fix three concentric balls B_1 \subset B_2 \subset B_3. The three spheres theorem claims that if  |u| < 1  on $B_3$ and |u| < \varepsilon  on B_1, then |u| < C \varepsilon^\alpha on B_2, where \alpha \in (0,1) and C>0 depend on L and the balls, but not on u.We are going to demonstrate how to apply this theorem.
Alexander Logunov