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Riku
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Scaled Harnack inequality $\sup_{B_r} v \le c\,(1-r)^{-p}\, \inf_{B_r} v$

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Riku
  • 839
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  • 17

Scaled Harnack inequality

Where can I find a proof of the following scaled version of Harnack inequality?

Let $v$ be a non-negative solution of ${L}u = 0$ in $B_1$, with $L$ a uniformly elliptic operator. Then, for $r<1$, there exist constants $c$ and $p$ such that $\sup_{B_r} v \le c\,(1-r)^{-p}\, \inf_{B_r} v.$