How to play with the three spheres theorem.
How to play with the three spheres theorem.

Alexander Logunov, IAS
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.