How to play with the three spheres theorem.
How to play with the three spheres theorem.
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Alexander Logunov, IAS
Please note the different time.Let u be a solution of second order elliptic differential equation Lu = 0.听Fix three concentric balls B_1 \subset B_2 \subset B_3.听The three spheres theorem claims that if听 |u| < 1听 on $B_3$ and |u| < \varepsilon听 on B_1, then |u| < C \varepsilon^\alpha听on B_2,听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.